2.626   ODE No. 626

\[ y'(x)=\frac {x}{\sqrt {x^2+1}+y(x)} \] Mathematica : cpu = 0.212384 (sec), leaf count = 88


\[\text {Solve}\left [\frac {1}{2} \left (\log \left (-\frac {y(x)^2}{x^2+1}-\frac {y(x)}{\sqrt {x^2+1}}+1\right )+\log \left (x^2+1\right )\right )=\frac {\tanh ^{-1}\left (\frac {3 \sqrt {x^2+1}+y(x)}{\sqrt {5} \left (\sqrt {x^2+1}+y(x)\right )}\right )}{\sqrt {5}}+c_1,y(x)\right ]\] Maple : cpu = 0.438 (sec), leaf count = 115


\[-\frac {4 \ln \left (\frac {36 \sqrt {x^{2}+1}}{y \relax (x )+\sqrt {x^{2}+1}}\right )}{3}+\frac {2 \ln \left (-\frac {1296 \left (\sqrt {x^{2}+1}\, y \relax (x )-x^{2}+y \relax (x )^{2}-1\right )}{11 \left (y \relax (x )+\sqrt {x^{2}+1}\right )^{2}}\right )}{3}-\frac {4 \sqrt {5}\, \arctanh \left (\frac {\left (3 \sqrt {x^{2}+1}+y \relax (x )\right ) \sqrt {5}}{5 y \relax (x )+5 \sqrt {x^{2}+1}}\right )}{15}+\frac {2 \ln \left (x^{2}+1\right )}{3}-c_{1} = 0\]