Problem with ordinary differental equation

Question

fiza fiza 2016-12-1

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https://ww2.mathworks.cn/matlabcentral/answers/314870-problem-with-ordinary-differental-equation

回答： Ghanim 2023-1-11

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..

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Answer 1

Karan Gill 2016-12-1

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https://ww2.mathworks.cn/matlabcentral/answers/314870-problem-with-ordinary-differental-equation#answer_245514

编辑：Karan Gill 2017-10-17

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".

subs: https://www.mathworks.com/help/symbolic/subs.html

double: https://www.mathworks.com/help/symbolic/double.html

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Karan Gill 2016-12-8

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 2017-1-9