\[ \boxed { 3\, \left ( \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\, \left ( y \left ( x \right ) \right ) ^{3}-6\,x \left ( 1+x \right ) y \left ( x \right ) -3\,{{\rm e}^{x}}=0} \]
Mathematica: cpu = 0.046006 (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 = 0.047 (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 \} \]