\[ 2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)-y(x)^3=0 \] ✗ Mathematica : cpu = 26.4484 (sec), leaf count = 0 , could not solve
DSolve[2*a^2*y[x] + a*y[x]^2 - y[x]^3 + (3*a + y[x])*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.444 (sec), leaf count = 415
\[ \left \{ y \left ( x \right ) ={\frac {1}{{{\rm e}^{ax}}}{\it RootOf} \left ( \int ^{{\it \_Z}}\!{\frac {1}{-{{\it \_f}}^{6}+{\it \_C1}} \left ( {{\it \_f}}^{8}-{\it \_C1}\,{{\it \_f}}^{2}+ \left ( \left ( -{{\it \_f}}^{6}+{\it \_C1} \right ) ^{2} \left ( \sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}-1 \right ) \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{ \left ( -{{\it \_f}}^{6}+{\it \_C1} \right ) ^{2} \left ( \sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}-1 \right ) }}}}{d{\it \_f}}a+a{\it \_C2}+{{\rm e}^{-ax}} \right ) },y \left ( x \right ) ={\frac {1}{{{\rm e}^{ax}}}{\it RootOf} \left ( \int ^{{\it \_Z}}\!{\frac {1}{-{{\it \_f}}^{6}+{\it \_C1}} \left ( -i\sqrt {3}{{\it \_f}}^{8}-{{\it \_f}}^{8}+i\sqrt {3}{\it \_C1}\,{{\it \_f}}^{2}+i\sqrt {3} \left ( \left ( -{{\it \_f}}^{6}+{\it \_C1} \right ) ^{2} \left ( \sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}-1 \right ) \right ) ^{{\frac {2}{3}}}+{\it \_C1}\,{{\it \_f}}^{2}- \left ( \left ( -{{\it \_f}}^{6}+{\it \_C1} \right ) ^{2} \left ( \sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}-1 \right ) \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{ \left ( -{{\it \_f}}^{6}+{\it \_C1} \right ) ^{2} \left ( \sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}-1 \right ) }}}}{d{\it \_f}}a+2\,a{\it \_C2}+2\,{{\rm e}^{-ax}} \right ) },y \left ( x \right ) ={\frac {1}{{{\rm e}^{ax}}}{\it RootOf} \left ( -\int ^{{\it \_Z}}\!{\frac {1}{-{{\it \_f}}^{6}+{\it \_C1}} \left ( -i\sqrt {3}{{\it \_f}}^{8}+{{\it \_f}}^{8}+i\sqrt {3}{\it \_C1}\,{{\it \_f}}^{2}+i\sqrt {3} \left ( \left ( -{{\it \_f}}^{6}+{\it \_C1} \right ) ^{2} \left ( \sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}-1 \right ) \right ) ^{{\frac {2}{3}}}-{\it \_C1}\,{{\it \_f}}^{2}+ \left ( \left ( -{{\it \_f}}^{6}+{\it \_C1} \right ) ^{2} \left ( \sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}-1 \right ) \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{ \left ( -{{\it \_f}}^{6}+{\it \_C1} \right ) ^{2} \left ( \sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}-1 \right ) }}}}{d{\it \_f}}a+2\,a{\it \_C2}+2\,{{\rm e}^{-ax}} \right ) } \right \} \]