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

y=ax+b when n=0

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

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