An asymptotic expansion

Question

The function $w(x)$ satisfies $$\frac{d^2w}{dx^2} + 2x\frac{dw}{dx} - 2\beta w = 0$$ with $$w(\infty)=0 \text{ and } 0<\beta < 1.$$ By writing $w(x)= exp(-x^2)f(x)$, obtain the first two terms of an asymptotic expansion for $w(x)$ as $x \to \infty $.