Problem: Find a uniformly valid approximation to the solution of $\epsilon y''(x) + x^2y' + x^2 = 0$ with boundary conditions $y(0) = 0, y(1) = -32$ in the limit $\epsilon \to 0^+$. Use only the variables and constants given in the problem; do not define additional constants. Place your final solution in a $\boxed{}$ LaTeX environment.
Solution: $\boxed{y(x,\epsilon) = -x - 31 \frac{\int_0^{x^3/(3\epsilon)} t^{-2/3} e^{-t} dt}{\Gamma(1/3)}}$