Problem: Find a uniformly valid approximation to the solution of $0.005 y''(x) + x^2y' + x = 0$ with boundary conditions $y(0) = 0, y(1) = -32$. 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: $\boxed{y(x) = -23.4198 \int_{0}^{x/0.005^{1/3}} e^{-s^3/3} ds - \int_{0}^{x/0.005^{1/3}} e^{-s^3/3} \left( \int_{0}^{s} t e^{t^3/3} dt \right) ds}$