Trouble using dsolve function

Hi,

I need help in solving a 2nd order diff equations. Since my equations are very long (almost 30 lines), I have written a similar code below to explain my question.

z= a*x+b*x^2+c+........; S =dsolve('D2y +5*z+ 2*x + 10*z^2','x')

Now since my z equation is very long I need to substitute z in the dsolve function. I tried using inline function by doing this

z = inline ('a*x+b*x^2+c+........')

 but I am not sure if the dsolve program is taking the value of z. Its running though, and it says no explicit solution found and returns me an empty symbol. Am I doing the right thing or is there any other way to do it.

Answer 1

[Walter Roberson]

z = a*x+b*x^2+c+........; 
eqn = subs(sym('D2y +5*z+ 2*x + 10*z^2'), z, z);
S = dsolve(eqn, x);

Myself, I would probably toss in a simplify() around the subs() .

[Nitin]

Hey Walter,

Thank you for your reply. I tried you subs and simplify function like this for my equation

eqn1 = simplify(subs(sym('(D2p1/((8.314)*(573.15)))+(((((p1+p2+p3)*Dp2-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*N1+(p2/(p1+p2+p3))*(-N1/r)-N2*(((p1+p2+p3)*Dp1-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)-(p1/(p1+p2+p3))*(-N2/r))/(1.7241e-05)+((((p1+p2+p3)*Dp3-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*N1+(-N1/r)*(p3/(p1+p2+p3))-(p1/(p1+p2+p3))*(-k*p1/(R*T)-N3/r)-N3*(((p1+p2+p3)*Dp1-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2))/(1.0642e-05))+(-N1/r)/(5.6164e-08)+((9.5703e-18)/((8.314)*(573.15)*(0.00001027)*(5.6164e-08))*((((p1+p2+p3)*Dp1-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*(p1+p2+p3)*(Dp1+Dp2+Dp3)+(p1/(p1+p2+p3))*(Dp1+Dp2+Dp3)*(p1+p2+p3)+(p1/(p1+p2+p3))*((Dp1+Dp2+Dp3))^2))'), N1, N1, N2, N2, N1, N1, N3, N3, N1));

But I get an error

??? Error using ==> sym.subs

Too many input arguments.

Can you show me the right syntax for this.

Thanks once again.

[Walter Roberson]

The syntax I used is valid for the case of exactly one thing to substitute in. When you have multiple things to substitute in, you must form lists.

eq1 = simplify(subs(...., {'N1', 'N2', 'N3'}, {N1, N2, N3}))

Answer 2

[Nitin]

Hey Walter,

I fixed the problem. Many thanks for your help. Can you tell me one more thing. After I run my program, it gives me this message Warning: Empty equation In dsolve at 91 In secondorder at 92

can you tell me what this means. I searched on the matlab website and there is no such warnings listed.

thanks, Nitin

Answer 3

[Nitin]

Hey Walter,

This is my code

eqn1 = simplify(subs(sym('(D2p1/((8.314)*(573.15)))+(((((p1+p2+p3)*Dp2-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*N1+(p2/(p1+p2+p3))*(-N1/r)-N2*(((p1+p2+p3)*Dp1-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)-(p1/(p1+p2+p3))*(-N2/r))/(1.7241e-05)+((((p1+p2+p3)*Dp3-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*N1+(-N1/r)*(p3/(p1+p2+p3))-(p1/(p1+p2+p3))*(-k*p1/(R*T)-N3/r)-N3*(((p1+p2+p3)*Dp1-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2))/(1.0642e-05))+(-N1/r)/(5.6164e-08)+((9.5703e-18)/((8.314)*(573.15)*(0.00001027)*(5.6164e-08))*((((p1+p2+p3)*Dp1-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*(p1+p2+p3)*(Dp1+Dp2+Dp3)+(p1/(p1+p2+p3))*(Dp1+Dp2+Dp3)*(p1+p2+p3)+(p1/(p1+p2+p3))*((Dp1+Dp2+Dp3))^2))'), {N1 N1 N2 N2 N1 N1 N3 N3 N1}, {N1 N1 N2 N2 N1 N1 N3 N3 N1}));

eqn2 = simplify(subs(sym('(D2p2/((8.314)*(573.15)))+(((((p1+p2+p3)*Dp1-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*N2+(p1/(p1+p2+p3))*(-N2/r)-N1*(((p1+p2+p3)*Dp2-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)-(p2/(p1+p2+p3))*(-N1/r))/(1.7241e-05)+((p3/(p1+p2+p3))*(-N2/r)+N2*(((p1+p2+p3)*Dp3-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)-(p2/(p1+p2+p3))*(-k*p1/(R*T)-N3/r)-N3*(((p1+p2+p3)*Dp2-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2))/(6.5157e-06))+(-N2/r)/(3.3910e-08)+((9.5703e-18)/((8.314)*(573.15)*(0.00001027)*(3.3910e-08))*((((p1+p2+p3)*Dp2-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*(p1+p2+p3)*(Dp1+Dp2+Dp3)+(p2/(p1+p2+p3))*(Dp1+Dp2+Dp3)*(p1+p2+p3)+(p2/(p1+p2+p3))*((Dp1+Dp2+Dp3))^2))'), {N2 N2 N1 N1 N2 N2 N3 N3 N2},{N2 N2 N1 N1 N2 N2 N3 N3 N2}));

eqn3 = simplify(subs(sym('(D2p3/((8.314)*(573.15)))+(((((p1+p2+p3)*Dp1-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*N3+(-k*p1/(R*T)-N3/r)*(p1/(p1+p2+p3))-(p3/(p1+p2+p3))*(-N1/r)-N1*(((p1+p2+p3)*Dp3-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2))/(1.0642e-05)+((p2/(p1+p2+p3))*(-k*p1/(R*T)-N3/r)+N3*(((p1+p2+p3)*Dp2-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)-(p3/(p1+p2+p3))*(-N2/r)-N2*(((p1+p2+p3)*Dp3-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2))/(6.5157e-06))+(-k*p1/(R*T)-N3/r)/(1.9194e-08)+((9.5703e-18)/((8.314)*(573.15)*(0.00001027)*(1.9194e-08))*((((p1+p2+p3)*Dp3-(Dp1+Dp2+Dp3))/(p1+p2+p3)^2)*(p1+p2+p3)*(Dp1+Dp2+Dp3)+(p3/(p1+p2+p3))*(Dp1+Dp2+Dp3)*(p1+p2+p3)+(p3/(p1+p2+p3))*((Dp1+Dp2+Dp3))^2))'), {N3 N3 N1 N1 N3 N3 N2 N2 N3}, {N3 N3 N1 N1 N3 N3 N2 N2 N3}));

 S = dsolve(eqn1, eqn2, eqn3, r)

This on running gives me empty equation warning. I used the subs above like you said to substitute for the values of N1 , N2 and N3. Can you tell me where I am wrong. Does N1, N2 and N3 not substitute in these equations ?

Thanks, Nitin