# Differential equations basic problem

I know this is a basic Physics problems but somehow I can't solve it. We have the differential equation: $2x''x^2 - 4 x^2x' - 2 x^3 = 0$

We have to conclude that the system:

$x' = y$

$y' = 2y + x$

..is equivalent to the differential equation. How can I do it?

Thanks in advance!

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try to integrate whole equation – iostream007 May 16 '13 at 18:57

## 1 Answer

If $x \neq 0$, then solving for $x^{\prime\prime}$ we get $$x^{\prime\prime} = 2x^{\prime} + x$$ Now let $y = x^{\prime}$. Then $$y^{\prime} = x^{\prime\prime} = 2x^{\prime} + x = 2y + x$$

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@alo: Thank you! Let to ask just one thing.. Can I solve the equation for x'' in Maxima or Wolfram Alpha? – pluralism May 16 '13 at 19:59
Yes, you should be able to solve it in Maxima, not sure about alpha. Or you should be able to solve it by hand, see. – al0 May 16 '13 at 21:29
@pluralism: See WA Solution – Amzoti May 17 '13 at 1:19