Differential Equation isolation

[Lanza52]

Solve the differential equation:

$$\frac{dy}{dx}-\frac{y}{x}=3x^{2}$$

Where y(1)=3

Can't figure out how to isolate each side. Played with it forever to no success. Any tips?

 

[rock.freak667]

...whenever you have a function of the form:

$$\frac{dy}{dx}+Py=Q$$ where both P and Q are functions of x..
you multiply throughout by $e^{\int P dx}$ and then integrate both sides with respect to x...

HINT: When you multiply throughout by $e^{\int P dx}$ and then integrate both sides with respect to x

The left hand side becomes [itex]ye^{\int P dx}[/tex]

 

[robbondo]

If you want to use separation of variables you can solve the complimentary equation and use variation of parameters.