\[ -a x^2-b x-c+3 y(x) y''(x)-2 y'(x)^2=0 \] ✗ Mathematica : cpu = 0.0478507 (sec), leaf count = 0 , could not solve
DSolve[-c - b*x - a*x^2 - 2*Derivative[1][y][x]^2 + 3*y[x]*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.968 (sec), leaf count = 207
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -2\,b\arctan \left ( {\frac {2\,ax+b}{\sqrt {4\,ac-{b}^{2}}}} \right ) -2\,\int ^{{\it \_Z}}\!{\frac {b}{\sqrt {4\,{{\it \_f}}^{4/3}{\it \_C1}\,{b}^{2}-36\,c{{\it \_f}}^{2}a+9\,{b}^{2}{{\it \_f}}^{2}-2}}}{d{\it \_f}}\sqrt {4\,ac-{b}^{2}}+{\it \_C2}\,\sqrt {4\,ac-{b}^{2}} \right ) \left ( a{x}^{2}+bx+c \right ) ^{{\frac {3}{2}}},y \left ( x \right ) ={\it RootOf} \left ( -2\,b\arctan \left ( {\frac {2\,ax+b}{\sqrt {4\,ac-{b}^{2}}}} \right ) +2\,\int ^{{\it \_Z}}\!{\frac {b}{\sqrt {4\,{{\it \_f}}^{4/3}{\it \_C1}\,{b}^{2}-36\,c{{\it \_f}}^{2}a+9\,{b}^{2}{{\it \_f}}^{2}-2}}}{d{\it \_f}}\sqrt {4\,ac-{b}^{2}}+{\it \_C2}\,\sqrt {4\,ac-{b}^{2}} \right ) \left ( a{x}^{2}+bx+c \right ) ^{{\frac {3}{2}}} \right \} \]