Help Finding Explicit Solution Non Linear Differential Equation

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Edmund Timisora
Edmund Timisora on 18 Nov 2021
Commented: Edmund Timisora on 19 Nov 2021
Hello!
I am wondering if anyone has any advice to try to find an explicit solution for the following non-linear differential equation system:
Where a, b, c and d are constants.
With x(t) y(t).
I have been trying to use 'dsolve', and I am getting 'Warning: Unable to find explicit solution'
Is there any method to try to arrange these equations to find an explicit solution? Or define some constrains in the solver to find a solution for some restricted domain?
Any tips/help are really apreciated!
Thanks

Answers (1)

John D'Errico
John D'Errico on 19 Nov 2021
There is no assurance that ever nonlinear differential equatino you may choose to pose has an analytical solution. In fact, I not that just as the symbolic tolbox fails to find a solution, mathematica also seems stumped by it.
Do you have a domein of interest? Do you have known values for the constants? If so, then you can use a numerical solver, like ODE45. That should be fairly simple, as long as you do not pass through a singularity at y==0.
  1 Comment
Edmund Timisora
Edmund Timisora on 19 Nov 2021
Thanks for the answer.
By using simulink, I found the solutions are some kind of expirals (in the xy plot),
I know the constants a,b,c and d are >0.
And the region of interest is x and y > 0. (same for initial conditions).
I would like to find some expressions to try to understand how the parameters and initial conditions conditions affect the solution.

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