Second order non-linear differential equation

Is there a standard solution to the follwoing equation or it should be worked out from first principles (e.g. integration by parts if possible)

$\displaystyle ky^{(n-1)}\frac{d^{2}y}{dx^{2}}=0$

where $\displaystyle k$ and $\displaystyle n$ are constants.

Re: Second order non-linear differential equation

Well Assuming $\displaystyle k \not = 0 $ then $\displaystyle k y^{n-1} \frac{d^2y}{dx^2} = 0 $ imples that either $\displaystyle y^{n-1} = 0 $ or $\displaystyle \frac{d^2y}{dx^2} = 0 $, which would mean that the only solutions are $\displaystyle y = 0 $ and $\displaystyle y = p_0 x + p_1 $

Re: Second order non-linear differential equation