real analysis - Solving differential equation by using power series.

Find, using the power series: $$y(x)=\sum_{k=0}^\infty a_{k}x^k$$ a solution for the following differential equation: $$y'(x) = -x^2y(x),\,\, y(0)=1$$
What's the convergence radius of the constructed power series? Also give a closed formula.

So far I've come up with $\sum_{k=0}^\infty a_{k+1}(k+1)x^{k} = \sum_{k=0}^\infty -a_{k}x^{k+2}$.
Usually I try to find a recursive formula for the coefficients and then try and guess a formula for the coefficients, but I dont know how to compare the coefficients on this one as the powers of x don't coincide. How should I go on from here, all I know is that $a_0=0$.