Let $\displaystyle u = \frac{dy}{dx} $

And hence $\displaystyle \frac{du}{dx} = \frac{d^2y}{dx^2} $

You can then rearrange to get:

$\displaystyle \frac{du}{u^2} = -2xdx $

Which is solveable by some fairly simple integration

, don't forget to sub back into y.

Explicit just means you write it in the form $\displaystyle y(x) = blah blah $

This works as a general rule btw. If there is no "y" term in your 2nd order ODE, then you can transform it into a first order ODE using substitution as shown above.