# Problem with ordinary differental equation

1 view (last 30 days)
fiza fiza on 1 Dec 2016
Edited: Karan Gill on 17 Oct 2017
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..

Karan Gill on 1 Dec 2016
Edited: Karan Gill on 17 Oct 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".
fiza fiza on 9 Jan 2017
Edited: fiza fiza on 9 Jan 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);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%