$\displaystyle F''(\xi)+\frac{\xi}{2}F'(\xi) = F(\xi) $ with boundary conditions:

$\displaystyle F(0)=1, \ \ \ \ F\rightarrow0 \ \ as \ \ \xi\rightarrow\infty $

i got this problem when doing question about diffusion equation. they give the answer :

$\displaystyle F(\xi)=\frac{1}{\sqrt{\pi}}[(1+\frac{1}{2}\xi^{2})\int_{\xi}^{\infty}{e^{-\frac{x^{2}}{4}} dx} -\xi e^{-\frac{\xi^{2}}{4}}] $

but i just dont know how to get that?