#### 2.283   ODE No. 283

$3 \left (y(x)^2-x^2\right ) y'(x)+2 y(x)^3-6 x (x+1) y(x)-3 e^x=0$ Mathematica : cpu = 0.336903 (sec), leaf count = 477

$\left \{\left \{y(x)\to -\frac {3 \sqrt [3]{2} e^{2 x} x^2}{\sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}-\frac {e^{-2 x} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {3 \left (1+i \sqrt {3}\right ) e^{2 x} x^2}{2^{2/3} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}+\frac {\left (1-i \sqrt {3}\right ) e^{-2 x} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}{6 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {3 \left (1-i \sqrt {3}\right ) e^{2 x} x^2}{2^{2/3} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}+\frac {\left (1+i \sqrt {3}\right ) e^{-2 x} \sqrt [3]{\sqrt {-2916 e^{12 x} x^6+\left (-27 e^{7 x}+27 c_1 e^{4 x}\right ){}^2}-27 e^{7 x}+27 c_1 e^{4 x}}}{6 \sqrt [3]{2}}\right \}\right \}$ Maple : cpu = 0.059 (sec), leaf count = 407

$\left \{ y \left ( x \right ) ={\frac {1}{4\,{{\rm e}^{2\,x}}} \left ( -4\,{x}^{2} \left ( 1+i\sqrt {3} \right ) \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}}} \left ( -1+i\sqrt {3} \right ) \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}{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\,{x}^{2} \left ( -1+i\sqrt {3} \right ) \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 \}$