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Please help me solving the equation.

I found one of its solutions: $c_1=(xz)/y$

But another one is given as $c_2=(x^3/y)+x$ in the text book. But I cont find. Thank you.

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Hints:

  • Rewrite the equation in terms of $\dfrac{dy}{dx}$
  • Make the substitution $y = v~x$
  • You end up with a first order equation, use Integrating Factor
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  • $\begingroup$ What is the second one you said? How to make the substitution ? $\endgroup$ – Nrsnr Nov 2 '13 at 18:22
  • $\begingroup$ Where you see a $y$ substitute $vx$. Where you see a $dy/dx$, substitute $v + xv'$. $\endgroup$ – Amzoti Nov 2 '13 at 18:24
  • $\begingroup$ I get $dy/dx=3y/x+y^2/x^3$ and then? $\endgroup$ – Nrsnr Nov 2 '13 at 18:24
  • $\begingroup$ Okay now I get $x^2v'=2xv+v^2$ $\endgroup$ – Nrsnr Nov 2 '13 at 18:27
  • $\begingroup$ Now do the substitutions I listed above and you have a DEQ in terms of $dv/dx$, solve that and then substitute back. $\endgroup$ – Amzoti Nov 2 '13 at 18:27

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