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Random Poster 2010-07-08 12:16

A non-linear 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?

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 [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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