20100708, 12:16  #1 
Dec 2008
179 Posts 
A nonlinear differential equation
Consider the differential equation . Obviously is a solution, but are there any others?

20100708, 14:06  #2 
"William"
May 2003
New Haven
938_{16} Posts 
y=ax+b when n=0

20100718, 22:31  #3 
Apr 2010
2^{2}×37 Posts 
y = const. for any n; and if is a solution, then is a solution too, for arbitrary from the field of x. This does not help generalizing the solutions given so far, however.
Last fiddled with by ccorn on 20100718 at 22:33 
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