Hello,

Originally Posted by

**Deadstar** Where am I going wrong here?!?

Find the general solution of the following equation;

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

(...)

The answer given in the tutorial is (no working given) $\displaystyle y = \frac{x^3}{5} + Cx^{-2}$ and I have no idea how to get that though I figure the problem lies with the log bit... Any help?

Instead of dividing by $\displaystyle x$ try multiplying by $\displaystyle x$ :

$\displaystyle x \frac{\mathrm{d}y}{\mathrm{d}x} + 2y = x^3\implies

x^2 \frac{\mathrm{d}y}{\mathrm{d}x} + 2xy = x^4$

Now note that the LHS of the last equality is $\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}(x^2y)$ and you are done.