\[ 3 \left (y(x)^2-x^2\right ) y'(x)+2 y(x)^3-6 x (x+1) y(x)-3 e^x=0 \] ✓ Mathematica : cpu = 0.348255 (sec), leaf count = 477
DSolve[-3*E^x - 6*x*(1 + x)*y[x] + 2*y[x]^3 + 3*(-x^2 + y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {e^{-2 x} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}{3 \sqrt [3]{2}}-\frac {3 \sqrt [3]{2} e^{2 x} x^2}{\sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) e^{-2 x} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}{6 \sqrt [3]{2}}+\frac {3 \left (1+i \sqrt {3}\right ) e^{2 x} x^2}{2^{2/3} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) e^{-2 x} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}{6 \sqrt [3]{2}}+\frac {3 \left (1-i \sqrt {3}\right ) e^{2 x} x^2}{2^{2/3} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}\right \}\right \}\] ✓ Maple : cpu = 0.074 (sec), leaf count = 407
dsolve(3*(y(x)^2-x^2)*diff(y(x),x)+2*y(x)^3-6*x*(1+x)*y(x)-3*exp(x) = 0,y(x))
\[y \left (x \right ) = \frac {\left (4 x^{2} {\mathrm e}^{4 x}+\left (\left (4 \,{\mathrm e}^{3 x}-4 c_{1}+4 \sqrt {-4 x^{6} {\mathrm e}^{4 x}+{\mathrm e}^{6 x}-2 \,{\mathrm e}^{3 x} c_{1}+c_{1}^{2}}\right ) {\mathrm e}^{4 x}\right )^{\frac {2}{3}}\right ) {\mathrm e}^{-2 x}}{2 \left (-4 \left (-{\mathrm e}^{3 x}+c_{1}-\sqrt {-4 x^{6} {\mathrm e}^{4 x}+{\mathrm e}^{6 x}-2 \,{\mathrm e}^{3 x} c_{1}+c_{1}^{2}}\right ) {\mathrm e}^{4 x}\right )^{\frac {1}{3}}}\]