Problem with ordinary differental equation

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fiza fiza
fiza fiza 2016년 12월 1일
답변: Ghanim 2023년 1월 11일
Good Afternoon,
I have a problem on how to solve differential equation which is dsdx and dxdPO2_rbc. This is the equation that I want to solve:
dPO2dt= (Qb*(O2_bloodin - O2_blood)+ (DO2_m * (PO2_g - PO2,b)))./ (Vb * (alpha_O2 + (cap_b * dsdx * dxdp))); %.... equation (1)
which:
a1= -8532;
a2= 2121;
a3= -67.07;
a4= 936000;
a5= -31350;
a6= 2396;
a7= -67.10;
T= 37;
r= 0.69;
H_rbc= 61*exp(-9);
ph_virt= -log(r*H_rbc);
PO2_rbc= 90 %mmHg;
pco2= 46 %mmhg;
I have problem with dsdx and dxdPO2, where
S(x)=(a1*x + a2*x^2 + a3*x^3 + x^4)/ (a4 + a5*x + a6*x^2 + a7*x^3 + x^4) %.......(equation 2)
x= PO2_rbc * (10^(0.024*(37-T) + 0.4*(ph_virt - 7.4)+ 0.06*(log(40/PCO2)))) %.........(equation 3)
I try to differentiate S with respect to x using 'diff', and differentiate x with respect to PO2_rbc, but the result is in symbolic (sym) form. Hence, it cannot be solved in equation (1).
Could somebody help me with this problem? I mean, should I use 'diff' to solve dSdx and dxdPO2_rbc, or another method?
Thanks..

채택된 답변

Karan Gill
Karan Gill 2016년 12월 1일
편집: Karan Gill 2017년 10월 17일
I think what you're asking is how to go from symbolic to numeric form? Use the "subs" function to substitute symbolic values with numbers. Then convert the symbolic result to double using "double".
  댓글 수: 3
Karan Gill
Karan Gill 2016년 12월 8일
If you used "dsolve" so solve your problem symbolically, then why are you giving the solution from "dsolve" to "ode45". You already have the solution in double form. Just try to plot it using "plot" etc.
fiza fiza
fiza fiza 2017년 1월 9일
편집: fiza fiza 2017년 1월 9일
OK.. I changed to this code, and it works. Thanks... :-)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
syms x
S= ((a1*x) + (a2*(x^2)) + (a3*(x^3)) + (x^4))/ (a4 + a5*x + (a6*(x^2)) + (a7*(x^3)) + (x^4));
diff_S= jacobian(S,x);
diff_simple= simplify(diff_S);
eqn= Xa(8) * (10^(0.024*(37-T) + 0.4*(ph_virt - 7.4)+ 0.06*(log(40/Xa(3)))));
int_subs= subs(diff_simple,x,eqn);
h= double(int_subs);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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추가 답변 (1개)

Ghanim
Ghanim 2023년 1월 11일
d2y/dx^2+5y-4=0

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