Help: Analytical Solution to Coupled ODE

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    Coupled Ode
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The discussion centers on the challenge of finding an analytical solution to a coupled ordinary differential equation (ODE). The primary difficulty arises from the term g*f in the first and second equations, which complicates the solution process. It is established that the system can be simplified to a non-linear second-order ODE with one unknown function; however, closed-form solutions are generally unattainable. Numerical methods are recommended for solving the problem in most cases.

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Raz91
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Hello ,
I tried to solve this coupled ODE but with no success
Does anyone know if there is an analytical solution to this equation?

k55ohh.jpg


my problem is with the first & the second equations the term g*f is the my biggest problem i think
once i have the solution for g - the solution for h is trivial.

THANK YOU!
 
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The system can be reduced to a non-linear second order ODE with one unknown function only. But the solutions of this non-linear ODE cannot be expressed on a closed form in the general case (It might be possible in case of particular values of the parameters).
So, in the general case, the problem must be dealt with numerical means.
 
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