\[ 3 \left (y(x)^2-x^2\right ) y'(x)+2 y(x)^3-6 x (x+1) y(x)-3 e^x=0 \] ✓ Mathematica : cpu = 0.159563 (sec), leaf count = 477
\[\left \{\left \{y(x)\to -\frac {e^{-2 x} \sqrt [3]{\sqrt {\left (27 c_1 e^{4 x}-27 e^{7 x}\right ){}^2-2916 e^{12 x} x^6}+27 c_1 e^{4 x}-27 e^{7 x}}}{3 \sqrt [3]{2}}-\frac {3 \sqrt [3]{2} e^{2 x} x^2}{\sqrt [3]{\sqrt {\left (27 c_1 e^{4 x}-27 e^{7 x}\right ){}^2-2916 e^{12 x} x^6}+27 c_1 e^{4 x}-27 e^{7 x}}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) e^{-2 x} \sqrt [3]{\sqrt {\left (27 c_1 e^{4 x}-27 e^{7 x}\right ){}^2-2916 e^{12 x} x^6}+27 c_1 e^{4 x}-27 e^{7 x}}}{6 \sqrt [3]{2}}+\frac {3 \left (1+i \sqrt {3}\right ) e^{2 x} x^2}{2^{2/3} \sqrt [3]{\sqrt {\left (27 c_1 e^{4 x}-27 e^{7 x}\right ){}^2-2916 e^{12 x} x^6}+27 c_1 e^{4 x}-27 e^{7 x}}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) e^{-2 x} \sqrt [3]{\sqrt {\left (27 c_1 e^{4 x}-27 e^{7 x}\right ){}^2-2916 e^{12 x} x^6}+27 c_1 e^{4 x}-27 e^{7 x}}}{6 \sqrt [3]{2}}+\frac {3 \left (1-i \sqrt {3}\right ) e^{2 x} x^2}{2^{2/3} \sqrt [3]{\sqrt {\left (27 c_1 e^{4 x}-27 e^{7 x}\right ){}^2-2916 e^{12 x} x^6}+27 c_1 e^{4 x}-27 e^{7 x}}}\right \}\right \}\]
✓ Maple : cpu = 0.069 (sec), leaf count = 622
\[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{{\rm e}^{2\,x}}}\sqrt [3]{ \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}}}+2\,{\frac {{{\rm e}^{2\,x}}{x}^{2}}{\sqrt [3]{ \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}}}},y \left ( x \right ) =-{\frac {1}{4\,{{\rm e}^{2\,x}}}\sqrt [3]{ \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}}}-{{{\rm e}^{2\,x}}{x}^{2}{\frac {1}{\sqrt [3]{ \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}}}}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{2\,{{\rm e}^{2\,x}}}\sqrt [3]{ \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}}}-2\,{\frac {{{\rm e}^{2\,x}}{x}^{2}}{\sqrt [3]{ \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 ) ,y \left ( x \right ) =-{\frac {1}{4\,{{\rm e}^{2\,x}}}\sqrt [3]{ \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}}}-{{{\rm e}^{2\,x}}{x}^{2}{\frac {1}{\sqrt [3]{ \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}}}}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{2\,{{\rm e}^{2\,x}}}\sqrt [3]{ \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}}}-2\,{\frac {{{\rm e}^{2\,x}}{x}^{2}}{\sqrt [3]{ \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 ) \right \} \]