Help Finding Explicit Solution Non Linear Differential Equation

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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

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Answer 1

John D'Errico 2021-11-19

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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.

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Edmund Timisora 2021-11-19

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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