#### 2.626   ODE No. 626

$y'(x)=\frac {x}{\sqrt {x^2+1}+y(x)}$ Mathematica : cpu = 0.151535 (sec), leaf count = 88

$\text {Solve}\left [\frac {1}{2} \left (\log \left (-\frac {y(x)^2}{x^2+1}-\frac {y(x)}{\sqrt {x^2+1}}+1\right )+\log \left (x^2+1\right )\right )=c_1+\frac {\tanh ^{-1}\left (\frac {3 \sqrt {x^2+1}+y(x)}{\sqrt {5} \left (\sqrt {x^2+1}+y(x)\right )}\right )}{\sqrt {5}},y(x)\right ]$ Maple : cpu = 0.264 (sec), leaf count = 115

$\left \{ {\frac {2}{3}\ln \left ( -{\frac {1296}{11} \left ( \sqrt {{x}^{2}+1}y \left ( x \right ) -{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) \left ( y \left ( x \right ) +\sqrt {{x}^{2}+1} \right ) ^{-2}} \right ) }-{\frac {4\,\sqrt {5}}{15}{\it Artanh} \left ( {\sqrt {5} \left ( 3\,\sqrt {{x}^{2}+1}+y \left ( x \right ) \right ) \left ( 5\,y \left ( x \right ) +5\,\sqrt {{x}^{2}+1} \right ) ^{-1}} \right ) }-{\frac {4}{3}\ln \left ( 36\,{\frac {\sqrt {{x}^{2}+1}}{y \left ( x \right ) +\sqrt {{x}^{2}+1}}} \right ) }+{\frac {2\,\ln \left ( {x}^{2}+1 \right ) }{3}}-{\it \_C1}=0 \right \}$