Changing to polar coordinates bring the differential equation to form.
I have a differential equation and the problem says to change to polar coordinate system by assuming and bring the equation to form. The answer is . This problem is under "Implicit Functions" in the book, so I suppose I should use the Implicit-function theorem. But I don't see what I can get from that. I did substitute and tried to simplify, but in vain. The only way I see to solve this after substitution is by applying trigonometry, but every time either are multiplied by some other trigonometric function (that can't be simplified to a constant) and it seems that just trigonometry is not enough. Could you explain how such problems are solved? I couldn't find examples on the internet either.