Trying to solve the following:
DSolve[{y''[x] + y[x] y'[x] == 0, y[0] == 1, y'[0] == -1}, y[x], x]
leads Mathematica to declare that no analytic solution exists {}
along with the error:
DSolve::bvfail: For some branches of the general solution, unable to solve the conditions.
Yet, by performing a very simple substitution of $u = y'$ and solving by hand, we arrive at the remarkably simple solution of $y(x)=\tan\left(\frac{\pi}{4} - \frac{x}{2}\right)$. Indeed, using Maple to compute the solution yields this answer directly. Why is Mathematica unable to solve this DE symbolically while Maple can?