# Differential equation parametrisation with integrating factor

1. Feb 12, 2013

### Perrault

1. The problem statement, all variables and given/known data

Use parametrisation first, derive the equation including y and p = $\frac{dy}{dx}$ and use the integrating factor method to reduce it to an exact equation. Leave the solution in implicit parametric form.

$(y')^{3}$ + y$^{2}$ = xyy'

3. The attempt at a solution

I'm really lost at this. I tried writing p=y'
p$^{3}$ + y$^{2}$=xyp
$\frac{p^{3}+y^{2}}{yp}$ = x
$\frac{p^{3}}{yp}$ + $\frac{y^{2}}{yp}$ = x
$\frac{p^{2}}{y}$ + $\frac{y}{p}$ = x

And I don't really know what to do from there. Some facebook rumors propose that the integrating factor be $\frac{1}{y^{3}}$