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do you have any strategy to suggest in order to solve the following system of partial differential equations inx(s,t)andy(s,t)?

[tex]\frac{\partial x}{\partial t} = x - \frac{1}{2}\sin(2x)[/tex]

[tex]\frac{\partial y}{\partial t} = y \; \sin^2(x)[/tex]

(note that the partial differentiation is always with respect to t).

In case it might be useful, I can safely assume that the codomain ofx(s,t)andy(s,t)is [-1,1].

I already tried with Maple and Mathematica but they only give me numerical solutions.

An approximation would be ok for me, as long as I get a closed form forxandy.

I was also wondering if you think there might exist another system of coordinates in which this system is easier to solve

Thanks.

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# System of two differential equations with trigonometric functions

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