\[ 3 \left (y(x)^2-x^2\right ) y'(x)+2 y(x)^3-6 x (x+1) y(x)-3 e^x=0 \] ✓ Mathematica : cpu = 0.0597815 (sec), leaf count = 501
\[\left \{\left \{y(x)\to -\frac {e^{-2 x} \sqrt [3]{\sqrt {e^{8 x} \left (-2 c_1 e^{3 x}+c_1^2-4 e^{4 x} x^6+e^{6 x}\right )}+c_1 e^{4 x}-e^{7 x}}}{\sqrt [3]{2}}-\frac {\sqrt [3]{2} e^{2 x} x^2}{\sqrt [3]{\sqrt {e^{8 x} \left (-2 c_1 e^{3 x}+c_1^2-4 e^{4 x} x^6+e^{6 x}\right )}+c_1 e^{4 x}-e^{7 x}}}\right \},\left \{y(x)\to \frac {e^{-2 x} \left (\sqrt [3]{2} \left (1-i \sqrt {3}\right ) \left (\sqrt {e^{8 x} \left (-2 c_1 e^{3 x}+c_1^2-4 e^{4 x} x^6+e^{6 x}\right )}+c_1 e^{4 x}-e^{7 x}\right ){}^{2/3}+2 \left (1+i \sqrt {3}\right ) e^{4 x} x^2\right )}{2\ 2^{2/3} \sqrt [3]{\sqrt {e^{8 x} \left (-2 c_1 e^{3 x}+c_1^2-4 e^{4 x} x^6+e^{6 x}\right )}+c_1 e^{4 x}-e^{7 x}}}\right \},\left \{y(x)\to \frac {e^{-2 x} \left (\sqrt [3]{2} \left (1+i \sqrt {3}\right ) \left (\sqrt {e^{8 x} \left (-2 c_1 e^{3 x}+c_1^2-4 e^{4 x} x^6+e^{6 x}\right )}+c_1 e^{4 x}-e^{7 x}\right ){}^{2/3}+2 \left (1-i \sqrt {3}\right ) e^{4 x} x^2\right )}{2\ 2^{2/3} \sqrt [3]{\sqrt {e^{8 x} \left (-2 c_1 e^{3 x}+c_1^2-4 e^{4 x} x^6+e^{6 x}\right )}+c_1 e^{4 x}-e^{7 x}}}\right \}\right \}\]
✓ Maple : cpu = 0.069 (sec), leaf count = 407
\[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{{\rm e}^{2\,x}}} \left ( 4\,{x}^{2} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( \left ( 4\,{{\rm e}^{3\,x}}-4\,{\it \_C1}+4\,\sqrt {-4\,{x}^{6} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( {{\rm e}^{3\,x}} \right ) ^{2}-2\,{{\rm e}^{3\,x}}{\it \_C1}+{{\it \_C1}}^{2}} \right ) \left ( {{\rm e}^{2\,x}} \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\, \left ( -{{\rm e}^{3\,x}}+{\it \_C1}-\sqrt {-4\,{x}^{6} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( {{\rm e}^{3\,x}} \right ) ^{2}-2\,{{\rm e}^{3\,x}}{\it \_C1}+{{\it \_C1}}^{2}} \right ) \left ( {{\rm e}^{2\,x}} \right ) ^{2}}}}},y \left ( x \right ) ={\frac {1}{4\,{{\rm e}^{2\,x}}} \left ( -4\, \left ( 1+i\sqrt {3} \right ) {x}^{2} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( i\sqrt {3}-1 \right ) \left ( \left ( 4\,{{\rm e}^{3\,x}}-4\,{\it \_C1}+4\,\sqrt {-4\,{x}^{6} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( {{\rm e}^{3\,x}} \right ) ^{2}-2\,{{\rm e}^{3\,x}}{\it \_C1}+{{\it \_C1}}^{2}} \right ) \left ( {{\rm e}^{2\,x}} \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\, \left ( -{{\rm e}^{3\,x}}+{\it \_C1}-\sqrt {-4\,{x}^{6} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( {{\rm e}^{3\,x}} \right ) ^{2}-2\,{{\rm e}^{3\,x}}{\it \_C1}+{{\it \_C1}}^{2}} \right ) \left ( {{\rm e}^{2\,x}} \right ) ^{2}}}}},y \left ( x \right ) =-{\frac {1}{4\,{{\rm e}^{2\,x}}} \left ( -4\, \left ( i\sqrt {3}-1 \right ) {x}^{2} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( 1+i\sqrt {3} \right ) \left ( \left ( 4\,{{\rm e}^{3\,x}}-4\,{\it \_C1}+4\,\sqrt {-4\,{x}^{6} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( {{\rm e}^{3\,x}} \right ) ^{2}-2\,{{\rm e}^{3\,x}}{\it \_C1}+{{\it \_C1}}^{2}} \right ) \left ( {{\rm e}^{2\,x}} \right ) ^{2} \right ) ^{{\frac {2}{3}}} \right ) {\frac {1}{\sqrt [3]{-4\, \left ( -{{\rm e}^{3\,x}}+{\it \_C1}-\sqrt {-4\,{x}^{6} \left ( {{\rm e}^{2\,x}} \right ) ^{2}+ \left ( {{\rm e}^{3\,x}} \right ) ^{2}-2\,{{\rm e}^{3\,x}}{\it \_C1}+{{\it \_C1}}^{2}} \right ) \left ( {{\rm e}^{2\,x}} \right ) ^{2}}}}} \right \} \]