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Problem with ordinary differental equation

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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)
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?

Risposta accettata

Karan Gill
Karan Gill il 1 Dic 2016
Modificato: Karan Gill il 17 Ott 2017
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".
  3 Commenti
Karan Gill
Karan Gill il 8 Dic 2016
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 il 9 Gen 2017
Modificato: fiza fiza il 9 Gen 2017
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);

Accedi per commentare.

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Ghanim il 11 Gen 2023

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