\[ a^2 y''(x)^2-2 a x y''(x)+y'(x)=0 \] ✗ Mathematica : cpu = 0.795138 (sec), leaf count = 0 , could not solve
DSolve[Derivative[1][y][x] - 2*a*x*Derivative[2][y][x] + a^2*Derivative[2][y][x]^2 == 0, y[x], x]
✓ Maple : cpu = 19.836 (sec), leaf count = 81
\[ \left \{ y \left ( x \right ) =\int \!{\it RootOf} \left ( -\int _{{\it \_g}}^{{\it \_Z}}\! \left ( x\sqrt {{x}^{2}-{\it \_f}}-{x}^{2}+2\,a{\it \_f} \right ) ^{-1}\,{\rm d}{\it \_f}+{\it \_C1} \right ) \,{\rm d}x+{\it \_C2},y \left ( x \right ) =\int \!{\it RootOf} \left ( -\int _{{\it \_g}}^{{\it \_Z}}\! \left ( x\sqrt {{x}^{2}-{\it \_f}}+{x}^{2}-2\,a{\it \_f} \right ) ^{-1}\,{\rm d}{\it \_f}+{\it \_C1} \right ) \,{\rm d}x+{\it \_C2} \right \} \]