\[ y''(x) \left (a x^2+2 b x+c+y(x)^2\right )^2+d y(x)=0 \] ✗ Mathematica : cpu = 45.6153 (sec), leaf count = 0 , could not solve
DSolve[d*y[x] + (c + 2*b*x + a*x^2 + y[x]^2)^2*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.776 (sec), leaf count = 336
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\!{\frac {a}{-{{\it \_f}}^{4}ac+{{\it \_f}}^{4}{b}^{2}+{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-c{{\it \_f}}^{2}a+{b}^{2}{{\it \_f}}^{2}+{\it \_C1}\,{a}^{2}+d}\sqrt { \left ( {{\it \_f}}^{2}+1 \right ) \left ( -{{\it \_f}}^{4}ac+{{\it \_f}}^{4}{b}^{2}+{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-c{{\it \_f}}^{2}a+{b}^{2}{{\it \_f}}^{2}+{\it \_C1}\,{a}^{2}+d \right ) }}{d{\it \_f}}\sqrt {ca-{b}^{2}}+{\it \_C2}\,\sqrt {ca-{b}^{2}}-a\arctan \left ( {(ax+b){\frac {1}{\sqrt {ca-{b}^{2}}}}} \right ) \right ) \sqrt {a{x}^{2}+2\,bx+c},y \left ( x \right ) ={\it RootOf} \left ( \int ^{{\it \_Z}}\!{\frac {a}{-{{\it \_f}}^{4}ac+{{\it \_f}}^{4}{b}^{2}+{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-c{{\it \_f}}^{2}a+{b}^{2}{{\it \_f}}^{2}+{\it \_C1}\,{a}^{2}+d}\sqrt { \left ( {{\it \_f}}^{2}+1 \right ) \left ( -{{\it \_f}}^{4}ac+{{\it \_f}}^{4}{b}^{2}+{\it \_C1}\,{{\it \_f}}^{2}{a}^{2}-c{{\it \_f}}^{2}a+{b}^{2}{{\it \_f}}^{2}+{\it \_C1}\,{a}^{2}+d \right ) }}{d{\it \_f}}\sqrt {ca-{b}^{2}}+{\it \_C2}\,\sqrt {ca-{b}^{2}}-a\arctan \left ( {(ax+b){\frac {1}{\sqrt {ca-{b}^{2}}}}} \right ) \right ) \sqrt {a{x}^{2}+2\,bx+c} \right \} \]