Problem: Find the leading order WKB approximation for the specific differential equation: $\epsilon^2 y'' = x y$ with initial conditions at $y(1)=1,y'(1)=1$ where $\epsilon$ is a small positive parameter ($0 < \epsilon \ll 1$
Solution: $\boxed{\frac{\left(\left(4 - 5 \epsilon\right) e^{\frac{4}{3 \epsilon}} + \left(5 \epsilon + 4\right) e^{\frac{4 x^{\frac{3}{2}}}{3 \epsilon}}\right) e^{- \frac{2 \left(x^{\frac{3}{2}} + 1\right)}{3 \epsilon}}}{8 \sqrt[4]{x}}}$