#### 2.671   ODE No. 671

$y'(x)=\frac {\left (x y(x)^2+1\right )^2}{x^4 y(x)}$ Mathematica : cpu = 0.329054 (sec), leaf count = 192

$\left \{\left \{y(x)\to -\frac {\sqrt {\sqrt {2} e^{\frac {2 \sqrt {2} (c_1 x+1)}{x}}-\frac {2 e^{\frac {2 \sqrt {2} (c_1 x+1)}{x}}}{x}-\frac {2}{x}-\sqrt {2}}}{\sqrt {2 e^{\frac {2 \sqrt {2} (c_1 x+1)}{x}}+2}}\right \},\left \{y(x)\to \frac {\sqrt {\sqrt {2} e^{\frac {2 \sqrt {2} (c_1 x+1)}{x}}-\frac {2 e^{\frac {2 \sqrt {2} (c_1 x+1)}{x}}}{x}-\frac {2}{x}-\sqrt {2}}}{\sqrt {2 e^{\frac {2 \sqrt {2} (c_1 x+1)}{x}}+2}}\right \}\right \}$ Maple : cpu = 0.148 (sec), leaf count = 237

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