Hi, I was wondering how to go about converting a homogeneous ODE of the form M(x,y)dx+N(x,y)dy=0 (where, by definition of a homogeneous ODE, M(tx,ty)=(t^a)M(x,y) and N(tx,ty)=(t^a)N(x,y) ) to polar coordinates. I wan to do this because using substitution of y/x=u and dy/dx=u+xdu/dx to make the ODE separable does not always result in the easiest integration towards the final steps. I figure by making x=rcosθ and y=rsinθ, I can completely isolate and remove r and make the ODE separable in terms of r and θ. I am completely able to convert half of the equation, but have very little idea how to transform dy/dx into something in terms of r and θ. Can anyone explain a little on how to to this?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks,

Mike

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# Coveting ODE to polar coordinates

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