#### 2.310   ODE No. 310

$\left (5 x^2 y(x)+2 y(x)^3\right ) y'(x)+x^3+5 x y(x)^2=0$ Mathematica : cpu = 0.170671 (sec), leaf count = 159

$\left \{\left \{y(x)\to -\frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}}\right \}\right \}$ Maple : cpu = 0.084 (sec), leaf count = 125

$\left \{ y \left ( x \right ) =-{\frac {1}{2}\sqrt {-10\,{\it \_C1}\,{x}^{2}-2\,\sqrt {23\,{x}^{4}{{\it \_C1}}^{2}+2}}{\frac {1}{\sqrt {{\it \_C1}}}}},y \left ( x \right ) ={\frac {1}{2}\sqrt {-10\,{\it \_C1}\,{x}^{2}-2\,\sqrt {23\,{x}^{4}{{\it \_C1}}^{2}+2}}{\frac {1}{\sqrt {{\it \_C1}}}}},y \left ( x \right ) =-{\frac {1}{2}\sqrt {-10\,{\it \_C1}\,{x}^{2}+2\,\sqrt {23\,{x}^{4}{{\it \_C1}}^{2}+2}}{\frac {1}{\sqrt {{\it \_C1}}}}},y \left ( x \right ) ={\frac {1}{2}\sqrt {-10\,{\it \_C1}\,{x}^{2}+2\,\sqrt {23\,{x}^{4}{{\it \_C1}}^{2}+2}}{\frac {1}{\sqrt {{\it \_C1}}}}} \right \}$