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Second order ode with non constant coeffcients

  • Thread starter ice109
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Homework Statement



[tex] y''(x)-k y^2 y'(x)=0 [/tex]


The Attempt at a Solution



mathematica gives me this:

[tex]\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\}[/tex]

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 [itex]x^2[/itex]
 
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