Given that the general solution of $y''+2y'+xy=0$ is $y=C_1\int_0^\infty e^{-t^2}\cos\biggl(\dfrac{t^3}{3}-xt\biggr)dt+C_2\int_0^\infty\biggl(e^{-\frac{t^3}{3}+t^2-xt}+e^{-t^2}\sin\biggl(\dfrac{t^3}{3}-xt\biggr)\biggr)dt$ , find the general solution of $xy''-(2x+1)y'+x^2y=0$ .
Note that according to Particular solution to a Riccati equation $y' = 1 + 2y + xy^2$, both $xy''-(2x+1)y'+x^2y=0$ and $y''+2y'+xy=0$ come from the same Riccati equation.