Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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!

share|improve this question
    
try to integrate whole equation –  iostream007 May 16 '13 at 18:57

1 Answer 1

up vote 1 down vote accepted

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

share|improve this answer
    
@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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.