A non-linear differential equation

Random Poster · 2010-07-08, 12:16

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

y = const. for any n; 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 x. This does not help generalizing the solutions given so far, however.

2010-07-08, 12:16	#1
Random Poster Dec 2008 179 Posts	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?

2010-07-18, 22:31	#3
ccorn Apr 2010 2²×37 Posts	y = const. for any n; 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 x. This does not help generalizing the solutions given so far, however. Last fiddled with by ccorn on 2010-07-18 at 22:33

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2010-07-08, 14:06	#2
wblipp "William" May 2003 New Haven 938₁₆ Posts	y=ax+b when n=0