I am not getting the laplace inverse of the function [c1 * exp(x1 * x) + c2 * exp(x2 * x) + c3 * exp(x3 * x) + c4 * exp(x4 * x) - B]

Simplified Laplace domain solution U(s):

(13778255085568*pi)/1083060099146055625 - (1139231246113845979*pi*ilaplace((s*exp(x*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 - (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)))/((79*s^2*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/840000000 + (3480097038439061*s^3*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/4159478531998877723661057392640000000 + (104071602499319*s^4*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/188894659314785808547840000000 + (s*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/7000000000 + (247556594090527*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/412316860416000000), s, x))/126937211059536063344148480000000000 - (1139231246113845979*pi*ilaplace((s*exp(-x*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 - (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)))/((79*s^2*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/840000000 + (3480097038439061*s^3*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/4159478531998877723661057392640000000 + (104071602499319*s^4*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/188894659314785808547840000000 + (s*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/7000000000 + (247556594090527*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/412316860416000000), s, x))/126937211059536063344148480000000000 + (1139231246113845979*pi*ilaplace((s*exp(-x*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 + (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)))/((79*s^2*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/840000000 + (3480097038439061*s^3*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/4159478531998877723661057392640000000 + (104071602499319*s^4*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/188894659314785808547840000000 + (s*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/7000000000 + (247556594090527*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/412316860416000000), s, x))/126937211059536063344148480000000000 - (123295256776534774804966233128325*symsum((exp(x*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k))*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k)^2)/(229166667790884431462400*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k)^3 + 261007277882929575*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k)^2 + 19559452620709008343406162739200*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k) + 14855280471424563298789490688), k, 1, 4))/27726338538139024 - (724917264154726073040897397589606400*symsum((exp(x*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k))*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k)^3)/(229166667790884431462400*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k)^3 + 261007277882929575*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k)^2 + 19559452620709008343406162739200*root(s3^4 + (3480097038439061*s3^3)/2291666677908844314624 + (373066952146701971881984*s3^2)/2185503652485699 + (4722366482869645213696*s3)/18212530437380825 + 340239192168947305089597440/312214807497957, s3, k) + 14855280471424563298789490688), k, 1, 4))/247556594090527 - (1139231246113845979*pi*ilaplace((s*exp(x*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 + (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2))*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 + (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2))/((247556594090527*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 - (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/412316860416000000 + (247556594090527*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 + (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/412316860416000000 + (79*s^2*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 - (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/840000000 + (79*s^2*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 + (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/840000000 + (3480097038439061*s^3*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 - (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/4159478531998877723661057392640000000 + (3480097038439061*s^3*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 + (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/4159478531998877723661057392640000000 + (104071602499319*s^4*((2840975676094379*s^2)/253874422119072126688296960000000 - 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134/175)^(1/2)*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/188894659314785808547840000000 + (s*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 - (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2)*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/7000000000 + (s*((2840975676094379*s^2)/253874422119072126688296960000000 - 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134/175)^(1/2))*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/((s^2*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/7000000000 + (79*s^3*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/840000000 + (3480097038439061*s^4*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/4159478531998877723661057392640000000 + (104071602499319*s^5*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/188894659314785808547840000000 + (247556594090527*s*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/412316860416000000), s, x))/210000000000 - (401*pi*ilaplace((exp(-x*((2840975676094379*s^2)/253874422119072126688296960000000 - (4021*s)/5250 + (- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2)/420000000 - 134/175)^(1/2))*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728)^(1/2))/((s^2*(- (35509982516091408931288273822296218308543244604359*s^4)/365375409332725729550921208179070754913983135744 - (116982996636416788184613125*s^3)/38685626227668133590597632 + (61082633293916799827446325899938190625*s^2)/590295810358705651712 + 206904575974800000*s + 13867462734254388019921875/134217728... Output truncated. Text exceeds maximum line length for Command Window display.

Answer 1

[Hassaan]

% Define symbolic variables
syms c1 c2 c3 c4 x1 x2 x3 x4 B s

% Define the function in the Laplace domain
F(s) = c1/(s - x1) + c2/(s - x2) + c3/(s - x3) + c4/(s - x4) - B;

% Compute the inverse Laplace transform
f_t = ilaplace(F(s));

% Display the result
disp('The inverse Laplace transform is:');

The inverse Laplace transform is:

disp(f_t);

Please replace c1, c2, c3, c4, x1, x2, x3, x4, and B with the actual values if you have them. This code will give you the inverse Laplace transform of the function in terms of the time variable t, which is implicitly assumed by ilaplace.

Run this code in MATLAB to get the inverse Laplace transform of your function. If you're having trouble with the specific values of c1, c2, c3, c4, x1, x2, x3, x4, or B, ensure they are defined before you run the ilaplace function. If these coefficients are numerical and not symbolic, you should define them in MATLAB before computing the inverse Laplace transform.

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[Tapobrata]

Mr Hassaan this my code ,I am not getting any solution.kindly suggest further.

clear
clc
close all

syms s x %L M S P Q S s X m c kf x1 x2 x3 x4 c1 c2 c3 c4 ita gama Ps t D h

L = 210 * 10^6;
M = 321.6 * 10^6;
S = 4.7 * 10^(-9);
X = -3.2168e+08;
P = 0.1757 * 10^(-12);
Q = 0.1156996 * 10^(-6);
m = 19.75;
c = 0.03;
kf = 126084.79;
D = 0.802

D = 0.8020

h = 2

h = 2

Ps = 6444.44

Ps = 6.4444e+03

ita = 0.55

ita = 0.5500

x1 = sqrt((-(M - S * s^2 - X * s) + sqrt((M - S * s^2 - X * s)^2 - 4 * L * (c * s + m * s^2 + P * s^3 + Q * s^4 + kf))) / (2 * L));
x2 = sqrt((-(M - S * s^2 - X * s) - sqrt((M - S * s^2 - X * s)^2 - 4 * L * (c * s + m * s^2 + P * s^3 + Q * s^4 + kf))) / (2 * L));
x3 = -sqrt((-(M - S * s^2 - X * s) + sqrt((M - S * s^2 - X * s)^2 - 4 * L * (c * s + m * s^2 + P * s^3 + Q * s^4 + kf))) / (2 * L));
x4 = -sqrt((-(M - S * s^2 - X * s) - sqrt((M - S * s^2 - X * s)^2 - 4 * L * (c * s + m * s^2 + P * s^3 + Q * s^4 + kf))) / (2 * L));

gama = (c * s + m * s^2 + P * s^3 + Q * s^4 + kf);
B = -((((pi) * D * h) / s) + (Ps / s - ita)) / gama;

c1 = (-x1 * x2 * x4 * B) / ((x1 - x2) * (x2 - x3) * (x1 - x4));
c2 = (x1 * x3 * x4 * B) / ((x1 - x2) * (x2 - x3) * (x2 - x4));
c3 = (-x1 * x2 * x4 * B) / ((x1 - x3) * (x2 - x3) * (x3 - x4));
c4 = (x1 * x2 * x3 * B) / ((x1 - x4) * (x2 - x4) * (x3 - x4));

u_x = c1 * exp(x1 * x) + c2 * exp(x2 * x) + c3 * exp(x3 * x) + c4 * exp(x4 * x) - B;

u1 = ilaplace(c1 * exp(x1 * x), s, x);
u2 = ilaplace(c2 * exp(x2 * x), s, x);
u3 = ilaplace(c3 * exp(x3 * x), s, x);
u4 = ilaplace(c4 * exp(x4 * x), s, x);
u_B = ilaplace(-B, s, x);

% Combine the terms
U_s = simplify(u1 + u2 + u3 + u4 + u_B);
U_s = ilaplace(u_x, s, x);

disp('Simplified Laplace domain solution U(s):');

Simplified Laplace domain solution U(s):

disp(U_s);

[Tapobrata]

first line doesnt have the tolal picture uploaded. And in the solution have Laplacian veriable 's' is still there ,as I need exact values,how to get exact tems of the fuction with 's' being eliminated.

[Torsten]

I just ran the code with MATLAB online to show the result - it's not an answer to your question. But most probably, your function is simply too complicated to be handled symbolically.

[Walter Roberson]

I doubt that the inverse laplace transform exists for these expressions.

[Paul]

The problem is ill-posed.

syms s x %L M S P Q S s X m c kf x1 x2 x3 x4 c1 c2 c3 c4 ita gama Ps t D h
L = 210 * 10^6;
M = 321.6 * 10^6;
S = 4.7 * 10^(-9);
X = -3.2168e+08;
P = 0.1757 * 10^(-12);
Q = 0.1156996 * 10^(-6);
m = 19.75;
c = 0.03;
kf = 126084.79;
D = 0.802;
h = 2;
Ps = 6444.44;
ita = 0.55;
x1 = sqrt((-(M - S * s^2 - X * s) + sqrt((M - S * s^2 - X * s)^2 - 4 * L * (c * s + m * s^2 + P * s^3 + Q * s^4 + kf))) / (2 * L));
x2 = sqrt((-(M - S * s^2 - X * s) - sqrt((M - S * s^2 - X * s)^2 - 4 * L * (c * s + m * s^2 + P * s^3 + Q * s^4 + kf))) / (2 * L));
x3 = -sqrt((-(M - S * s^2 - X * s) + sqrt((M - S * s^2 - X * s)^2 - 4 * L * (c * s + m * s^2 + P * s^3 + Q * s^4 + kf))) / (2 * L));
x4 = -sqrt((-(M - S * s^2 - X * s) - sqrt((M - S * s^2 - X * s)^2 - 4 * L * (c * s + m * s^2 + P * s^3 + Q * s^4 + kf))) / (2 * L));
gama = (c * s + m * s^2 + P * s^3 + Q * s^4 + kf);
B = -((((pi) * D * h) / s) + (Ps / s - ita)) / gama;
c1 = (-x1 * x2 * x4 * B) / ((x1 - x2) * (x2 - x3) * (x1 - x4));
c2 = (x1 * x3 * x4 * B) / ((x1 - x2) * (x2 - x3) * (x2 - x4));
c3 = (-x1 * x2 * x4 * B) / ((x1 - x3) * (x2 - x3) * (x3 - x4));
c4 = (x1 * x2 * x3 * B) / ((x1 - x4) * (x2 - x4) * (x3 - x4));
u_x = c1 * exp(x1 * x) + c2 * exp(x2 * x) + c3 * exp(x3 * x) + c4 * exp(x4 * x) - B;

symvar(u_x)

ans = 

symvar(c1 * exp(x1 * x))

ans = 

At this point, u_x and the first input to ilaplace for u1 (and I suspect u2-u4) are both functions of s and x. If x is to be the "to" variable for the inverse transform, it shouldn't be seen in the expression to be inverse transformed.

%{
u1 = ilaplace(c1 * exp(x1 * x), s, x);
u2 = ilaplace(c2 * exp(x2 * x), s, x);
u3 = ilaplace(c3 * exp(x3 * x), s, x);
u4 = ilaplace(c4 * exp(x4 * x), s, x);
u_B = ilaplace(-B, s, x);
% Combine the terms
U_s = simplify(u1 + u2 + u3 + u4 + u_B);
U_s = ilaplace(u_x, s, x);
disp('Simplified Laplace domain solution U(s):');
disp(U_s);
%}