\[ a y'(x) \left | y'(x)\right | +b y'(x)+c y(x)+y''(x)=0 \] ✗ Mathematica : cpu = 36.0775 (sec), leaf count = 0 , could not solve
DSolve[c*y[x] + b*Derivative[1][y][x] + a*Abs[Derivative[1][y][x]]*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 1.023 (sec), leaf count = 59
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +a{\it \_b} \left ( {\it \_a} \right ) \left | {\it \_b} \left ( {\it \_a} \right ) \right | +{\it \_b} \left ( {\it \_a} \right ) b+c{\it \_a}=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]