Problem: Find a uniformly valid approximation to the solution of $\epsilon y''(x) + \frac{3x+1}{2x+1}y'(x) - y(x)^{2} = 0$ with boundary conditions $y(0)=0, y(1)=1$ 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: $\boxed{y(x)=\frac{9}{15-6x-\ln(\frac{3x+1}{4})}-\frac{9}{15+\ln(4)}e^{-x/\epsilon}}$