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 Random Poster 2010-07-08 12:16

A non-linear differential equation

Consider the differential equation $$y''y=nx^ny'$$. Obviously $$y=x^{n+1}$$ is a solution, but are there any others?

 wblipp 2010-07-08 14:06

y=ax+b when n=0

 ccorn 2010-07-18 22:31

[I]y[/I] = const. for any [I]n[/I]; and if $$y=y_1(x)$$ is a solution, then $$y=\alpha^{-(n+1)}y_1(\alpha x)$$ is a solution too, for arbitrary $$\alpha$$ from the field of [I]x[/I]. This does not help generalizing the solutions given so far, however.

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