#### 2.827   ODE No. 827

$y'(x)=\frac {x^2 y(x) \sqrt {x^2+y(x)^2}+x^3 \left (-\sqrt {x^2+y(x)^2}\right )+y(x)}{x}$ Mathematica : cpu = 0.189673 (sec), leaf count = 221

$\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\frac {1}{3} \left (-3 \sqrt {2} c_1-\sqrt {2} x^3\right )\right )-x^2 \tanh ^4\left (\frac {1}{3} \left (-3 \sqrt {2} c_1-\sqrt {2} x^3\right )\right )}}{2 \tanh ^2\left (\frac {1}{3} \left (-3 \sqrt {2} c_1-\sqrt {2} x^3\right )\right )-1}\right \},\left \{y(x)\to \frac {2 \sqrt {x^2 \tanh ^2\left (\frac {1}{3} \left (-3 \sqrt {2} c_1-\sqrt {2} x^3\right )\right )-x^2 \tanh ^4\left (\frac {1}{3} \left (-3 \sqrt {2} c_1-\sqrt {2} x^3\right )\right )}+x}{2 \tanh ^2\left (\frac {1}{3} \left (-3 \sqrt {2} c_1-\sqrt {2} x^3\right )\right )-1}\right \}\right \}$ Maple : cpu = 0.169 (sec), leaf count = 49

$\left \{ \ln \left ( 2\,{\frac {x \left ( \sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2}}+y \left ( x \right ) +x \right ) }{y \left ( x \right ) -x}} \right ) +{\frac {\sqrt {2}{x}^{3}}{3}}-\ln \left ( x \right ) -{\it \_C1}=0 \right \}$