How can i solve these Coupled differential Equations?

I am trying to solve this with odeint module. But the first equation is function of second equation. If i ignore dw/dz in first equation and second equation is function of first one. I can solve it simply using odeint. I can solve these equation through fsolve through forward differential. But is it possible i can use Odeint with fsolve? and solve first two equation simultaneously to find.

• As it is right now, your question is not clear enough and it looks like you want that somebody else solve your problem for you. I suggest that you edit your question adding what specific problem are you having with the solution in Python. Jul 31, 2021 at 16:46
• If your question is about how to solve these problems in Python, the answer is by using a numerical solver. You could take a look at SciPy's integrator. Jul 31, 2021 at 16:47
• I am trying to solve this with odeint module. But the first equation is function of second equation. If i ignore dw/dz in first equation and second equation is function of first one. I can solve it simply using odeint. I can solve these equation through fsolve through forward differential. But is it possible i can use Odeint with fsolve? and solve first two equation simultaneously to find. Jul 31, 2021 at 17:06
• The way the equations are normally presented are with the derivative in the left hand side. Did you try solving for the 3 derivatives to rearrange your system? Aug 1, 2021 at 2:22
• Must you use Odeint? A scan through the documentation seems to indicate it doesn't support implicitly-defined ODEs. A python wrapper for SUNDIALS IDA might work. Aug 1, 2021 at 15:24

I would simply replace $$\dfrac{d\omega}{dz}$$ in the first equation by its expression as given in the second equation, and then regroup on the left-hand side all the terms involving $$\dfrac{dT_a}{dz}$$.
Then, knowing the values of your overall state vector $$X=(T_a,\omega,T_s)$$, you have an explicit formulation of $$\dfrac{dX}{dz}$$.