Solution
= Solution
After division by $e^{-x^2/2}$, $f\prime\prime-2xf\prime+8f=2$. The initial data and evenness give $f=1-3x^2+x^4$, hence $y=e^{-x^2/2}(1-3x^2+x^4)$.
= Solution
After division by $e^{-x^2/2}$, $f\prime\prime-2xf\prime+8f=2$. The initial data and evenness give $f=1-3x^2+x^4$, hence $y=e^{-x^2/2}(1-3x^2+x^4)$.