I'm self-teaching through Tenenbaum & Pollard's "Ordinary Differential Equations", and for some reason I'm completely stuck on one of the problems, Ch.2, lesson 6, problem #6:(adsbygoogle = window.adsbygoogle || []).push({});

Find a 1-parameter family of solutions for [...] the differential equation:

6) yx^{2}dy-y^{3}dx = 2x^{2}dy.

I didn't have trouble with any of the previous problems, but the algebra is evading me here. The proffered solution is:

(cx + 1)y^{2}= (y-1)x, x =/ 0, y =/ 0; y = 0.

but I can't find any families that don't involve fractions, let alone this one. The subsequent problems also seem to have an algebra trick that I'm missing, so once I understand this one I'll be fine I think.

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# I Basic Separation of Variables problem

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