# Second order non-linear differential equation

• December 22nd 2012, 03:09 AM
JulieK
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)

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

where $k$ and $n$ are constants.
• December 22nd 2012, 03:28 AM
jakncoke
Re: Second order non-linear differential equation
Well Assuming $k \not = 0$ then $k y^{n-1} \frac{d^2y}{dx^2} = 0$ imples that either $y^{n-1} = 0$ or $\frac{d^2y}{dx^2} = 0$, which would mean that the only solutions are $y = 0$ and $y = p_0 x + p_1$
• December 22nd 2012, 07:57 AM
JulieK
Re: Second order non-linear differential equation
Thank you jakncoke!