# Ordinary homogeneous differential equation [closed]

How to solve this one

$y''=(2xy - \frac{5}{x})y' + 4y^2 - \frac{4y}{x^2}$

I know it's homogeneous. I've made replacement $x = e^t$ and $y = ze^{-2t}$ but I had no result.

## closed as off-topic by Daniel Moskovich, Johannes Hahn, Nik Weaver, user9072, Ilya BogdanovDec 24 '15 at 18:28

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• "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – Community, Ilya Bogdanov
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• MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics. – Chris Ramsey Dec 24 '15 at 17:53

$$y = \dfrac{a}{x^2} \tanh(b - a \ln(x))$$