#can anybody help me with this system of non linear ODE

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lost sun
slender rampartBOT
lost sun
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I have managed to solve it for the case when p=q only but for the rest getting a solution for u and v separately seems challenging.

steady dirge
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I figure you just differentiate either equation by t again and sub in v or u

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It’ll be a gross second order but self contained that’s easier to guess and check

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Or we’ll

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Maybe not