Series Solutions · Hard problem

The equation $y'' + (1+x^2)y = 0$ has the power-series solution with $y(0)=1$, $y'(0)=0$. Because the equation is unchanged under $x \to -x$ and $y'(0)=0$, only even powers of $x$ appear. Find $a_2 + a_4$. Express your answer as a common fraction.