#### 2.879   ODE No. 879

$y'(x)=\frac {x^2 \left (-\sqrt {x^2+y(x)^2}\right )+x y(x) \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)}$ Mathematica : cpu = 0.242861 (sec), leaf count = 239

$\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\sqrt {2} c_1+\sqrt {2} x-\sqrt {2} \log (x+1)\right )-x^2 \tanh ^4\left (\sqrt {2} c_1+\sqrt {2} x-\sqrt {2} \log (x+1)\right )}}{2 \tanh ^2\left (\sqrt {2} c_1+\sqrt {2} x-\sqrt {2} \log (x+1)\right )-1}\right \},\left \{y(x)\to \frac {2 \sqrt {x^2 \tanh ^2\left (\sqrt {2} c_1+\sqrt {2} x-\sqrt {2} \log (x+1)\right )-x^2 \tanh ^4\left (\sqrt {2} c_1+\sqrt {2} x-\sqrt {2} \log (x+1)\right )}+x}{2 \tanh ^2\left (\sqrt {2} c_1+\sqrt {2} x-\sqrt {2} \log (x+1)\right )-1}\right \}\right \}$ Maple : cpu = 0.16 (sec), leaf count = 55

$\left \{ \ln \left ( 2\,{\frac {x \left ( \sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2}}+y \left ( x \right ) +x \right ) }{y \left ( x \right ) -x}} \right ) +\sqrt {2}x-\sqrt {2}\ln \left ( 1+x \right ) -\ln \left ( x \right ) -{\it \_C1}=0 \right \}$