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Old 2010-07-08, 12:16   #1
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Default 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?
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Old 2010-07-08, 14:06   #2
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y=ax+b when n=0
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Old 2010-07-18, 22:31   #3
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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.

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