# Second order ode with non constant coeffcients

1. Feb 26, 2008

### ice109

1. The problem statement, all variables and given/known data

$$y''(x)-k y^2 y'(x)=0$$

3. The attempt at a solution

mathematica gives me this:

$$\left\{\left\{y(x)\to\text{InverseFunction}\left[-\frac{2\sqrt{3}\tan^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2\sqrt[3]{k}\text{\#1}}{3^{5/6}\sqrt[3]{c_1}}\right)-2\log\left(3^{2/3}\sqrt[3]{k}\text{\#1}+3\sqrt[3]{c_1}\right)+\log\left(\sqrt[3]{3}k^{2/3}\text{\#1}^2-3^{2/3}\sqrt[3]{k}\sqrt[3]{c_1}\text{\#1}+3c_1^{2/3}\right)}{23^{2/3}\sqrt[3]{k}c_1^{2/3}}\&\right]\left[x+c_2\right]\right\}\right\}$$

yes something so ugly and long that i broke the latex parser on the website. so how do i solve this? i have no idea where to begin because none of the methods in my ODE book talk about function with coeffIcients like that $x^2$

Last edited: Feb 26, 2008