\[ 2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)-y(x)^3=0 \] ✗ Mathematica : cpu = 26.3566 (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 = 0.352 (sec), leaf count = 775
\[ \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 ( -{{\it \_f}}^{12}+2\,{\it \_C1}\,{{\it \_f}}^{6}-{{\it \_C1}}^{2}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_f}}^{12}-2\,\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{\it \_C1}\,{{\it \_f}}^{6}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_C1}}^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-{{\it \_f}}^{12}+2\,{\it \_C1}\,{{\it \_f}}^{6}-{{\it \_C1}}^{2}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_f}}^{12}-2\,\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{\it \_C1}\,{{\it \_f}}^{6}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_C1}}^{2}}}}}{d{\it \_f}}a+{\it \_C2}\,a+{{\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 ( -{{\it \_f}}^{12}+2\,{\it \_C1}\,{{\it \_f}}^{6}-{{\it \_C1}}^{2}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_f}}^{12}-2\,\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{\it \_C1}\,{{\it \_f}}^{6}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_C1}}^{2} \right ) ^{{\frac {2}{3}}}+{\it \_C1}\,{{\it \_f}}^{2}- \left ( -{{\it \_f}}^{12}+2\,{\it \_C1}\,{{\it \_f}}^{6}-{{\it \_C1}}^{2}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_f}}^{12}-2\,\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{\it \_C1}\,{{\it \_f}}^{6}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_C1}}^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-{{\it \_f}}^{12}+2\,{\it \_C1}\,{{\it \_f}}^{6}-{{\it \_C1}}^{2}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_f}}^{12}-2\,\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{\it \_C1}\,{{\it \_f}}^{6}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_C1}}^{2}}}}}{d{\it \_f}}a+2\,{\it \_C2}\,a+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 ( -{{\it \_f}}^{12}+2\,{\it \_C1}\,{{\it \_f}}^{6}-{{\it \_C1}}^{2}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_f}}^{12}-2\,\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{\it \_C1}\,{{\it \_f}}^{6}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_C1}}^{2} \right ) ^{{\frac {2}{3}}}-{\it \_C1}\,{{\it \_f}}^{2}+ \left ( -{{\it \_f}}^{12}+2\,{\it \_C1}\,{{\it \_f}}^{6}-{{\it \_C1}}^{2}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_f}}^{12}-2\,\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{\it \_C1}\,{{\it \_f}}^{6}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_C1}}^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-{{\it \_f}}^{12}+2\,{\it \_C1}\,{{\it \_f}}^{6}-{{\it \_C1}}^{2}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_f}}^{12}-2\,\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{\it \_C1}\,{{\it \_f}}^{6}+\sqrt {{\frac {{\it \_C1}}{-{{\it \_f}}^{6}+{\it \_C1}}}}{{\it \_C1}}^{2}}}}}{d{\it \_f}}a+2\,{\it \_C2}\,a+2\,{{\rm e}^{-ax}} \right ) } \right \} \]