Question

solve inseries d2y/dx2+x2y=0

Answer 1

separate variables

\[\frac{ dy^2}{y} = - x^2 dx^2\]
integrate twice
\[(\ln y +m) dy = (-\frac{x^3}{3} + k) dx\]
\[y \ln y - y + my = -\frac{x^4}{12} +kx +C\]
\[y = \frac{C +kx -x^4}{12( \ln y - 1+m)}\]

because of the ln(y) you cant algebraically solve for 'y' explicitly using elementary functions