- #1
obstinatus
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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:
Find a 1-parameter family of solutions for [...] the differential equation:
6) yx2dy-y3dx = 2x2dy.
I didn't have trouble with any of the previous problems, but the algebra is evading me here. The proffered solution is:
(cx + 1)y2 = (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.
Find a 1-parameter family of solutions for [...] the differential equation:
6) yx2dy-y3dx = 2x2dy.
I didn't have trouble with any of the previous problems, but the algebra is evading me here. The proffered solution is:
(cx + 1)y2 = (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.