Substitution to make it seperable

[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.

 

[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" for the rest really.

 

[Augmented]

thank you, I solved them all.