y''-x^{2}y=0, (y''=d^{2}y/dx^{2})

when try to find solution, usually assuming solution form is y=e^{lambda X}, and lambda =x, -x, then general solution is y=c_{1}e^{x^2}+ c_{2}e^{-x^2}. however, I was told this is wrong approach to solve.

Then how can I get correct general solution?