# Substitution to make it seperable

1. Jul 13, 2009

### Augmented

$$\acute{y}+xy^{3}+\frac{y}{x}=0$$
$$y(1)=2$$
using substitution $$u=y^{-2}$$

$$e^{y}\acute{y}=e^{-x}-e^{y}$$
$$y(0)=0$$
using substitution $$u=e^{y}$$

i could not make these equations seperable and solve for the IVP.
Anyone has any idea?

Edit: these problems are not homework, but for self study for preparation to the midterm.

Last edited: Jul 13, 2009
2. Jul 13, 2009

### rock.freak667

$$\frac{dy}{dx}+xy^{3}+\frac{y}{x}=0$$

$$\frac{dy}{dx}+\frac{y}{x}= -xy^3$$

Now read http://en.wikipedia.org/wiki/Bernoulli_differential_equation" [Broken] for the rest really.

Last edited by a moderator: May 4, 2017
3. Jul 13, 2009

### Augmented

thank you, I solved them all.