Problem: Find the leading order WKB approximation for the lowest order normalized eigenfunction of the differential equation: $y'' = -E_1 (x+\pi)^4 y$ with boundary conditions at $y(0)=0, y(\pi)=0$ where $E$ is a positive real value. Normalization is: $\int_0^\pi [y(x)^2 (x+\pi)^4] dx = 1$.Put your final answer in a LaTeX \boxed{} environment.
Solution: $\boxed{y(x)=\sqrt{\frac{6}{7\pi^3 }}\frac{1}{(x +\pi)} \sin(\frac{x^3 + 3 \pi x^2 + 3x \pi^2}{7\pi^2}) } $