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 = 0.329682 (sec), leaf count = 239


\[\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )-x^2 \tanh ^4\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}}{-1+2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}\right \},\left \{y(x)\to \frac {x+2 \sqrt {x^2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )-x^2 \tanh ^4\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}}{-1+2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}\right \}\right \}\] Maple : cpu = 0.196 (sec), leaf count = 55


\[\ln \left (\frac {2 x \left (\sqrt {2 y \relax (x )^{2}+2 x^{2}}+y \relax (x )+x \right )}{y \relax (x )-x}\right )+\sqrt {2}\, x -\ln \relax (x )-\sqrt {2}\, \ln \left (1+x \right )-c_{1} = 0\]