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)));
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)
x= PO2_rbc * (10^(0.024*(37-T) + 0.4*(ph_virt - 7.4)+ 0.06*(log(40/PCO2))))
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?