Problem: Find a uniformly valid approximation to the solution of $\epsilon y'' + (\cosh(x))(x^2 + 1)y' - x^3 y = 0$ with boundary conditions $y(0) = 1, y(1) = 1$ in the limit $\epsilon \ll 0+$. 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: $\boxed{y(x) = (1-\exp\left(\int_1^0 \frac{t^3}{\cosh(t)(t^2 + 1)}\ dt\right))e^{-x/\epsilon} + \exp\left(\int_1^x \frac{t^3}{\cosh(t)(t^2 + 1)}\ dt\right)}$