Problem: Find the leading order behavior of $y''=(\cot x)^4 y$ in the limit of small x that satisfies the conditions $y(1) = 1; y'(1) = 1$. Leading order does not necessarily mean only one term. Use only the variables and constants given in the problem; do not define additional constants. Give your final answer in a \boxed latex environment.
Solution: $\boxed{y(x) \sim \frac{e}{2} x e^{-1/x} + \frac{1}{2e} x e^{1/x}}$