\[ 2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)-y(x)^3=0 \] ✗ Mathematica : cpu = 24.0319 (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 = 1.328 (sec), leaf count = 817
\[ \left \{ y \left ( x \right ) ={\frac {1}{{{\rm e}^{ax}}}{\it RootOf} \left ( \int ^{{\it \_Z}}\!{\frac {1}{-{{\it \_f}}^{6}+{{\it \_C1}}^{2}} \left ( - \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}{{\it \_f}}^{6}+ \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}{{\it \_C1}}^{2}-{{\it \_f}}^{2} \right ) {\frac {1}{\sqrt [3]{-{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}}}}}}{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}}^{2}} \left ( -i \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}\sqrt {3}{{\it \_f}}^{6}- \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}{{\it \_f}}^{6}+i \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}\sqrt {3}{{\it \_C1}}^{2}+ \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}{{\it \_C1}}^{2}+i\sqrt {3}{{\it \_f}}^{2}-{{\it \_f}}^{2} \right ) {\frac {1}{\sqrt [3]{-{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}}}}}}{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}}^{2}} \left ( -i \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}\sqrt {3}{{\it \_f}}^{6}+ \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}{{\it \_f}}^{6}+i \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}\sqrt {3}{{\it \_C1}}^{2}- \left ( -{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}} \right ) ^{{\frac {2}{3}}}{{\it \_C1}}^{2}+i\sqrt {3}{{\it \_f}}^{2}+{{\it \_f}}^{2} \right ) {\frac {1}{\sqrt [3]{-{ \left ( -{\it \_C1}\,{{\it \_f}}^{12}+2\,{{\it \_C1}}^{3}{{\it \_f}}^{6}+ \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{{\frac {5}{2}}}-{{\it \_C1}}^{5} \right ) \left ( -{{\it \_f}}^{6}+{{\it \_C1}}^{2} \right ) ^{-{\frac {7}{2}}}}}}}}{d{\it \_f}}a+2\,a{\it \_C2}+2\,{{\rm e}^{-ax}} \right ) } \right \} \]