#### 2.151   ODE No. 151

$\left (x^2+1\right ) y'(x)+(2 x y(x)-1) \left (y(x)^2+1\right )=0$ Mathematica : cpu = 0.48398 (sec), leaf count = 203

$\text {Solve}\left [c_1=\frac {\frac {1}{2} \left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right ) \sqrt [4]{1-\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2} \, _2F_1\left (\frac {1}{2},\frac {5}{4};\frac {3}{2};\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2}},y(x)\right ]$ Maple : cpu = 0.037 (sec), leaf count = 85

$\left \{ {\it \_C1}+{x{\frac {1}{\sqrt [4]{ \left ( {x}^{-1}+{{x}^{2} \left ( {\frac {y \left ( x \right ) {x}^{4}}{{x}^{2}+1}}-{\frac {{x}^{3}}{{x}^{2}+1}} \right ) ^{-1}} \right ) ^{2}+1}}}}+{\frac {y \left ( x \right ) +x}{2\,xy \left ( x \right ) -2}{\mbox {_2F_1}({\frac {1}{2}},{\frac {5}{4}};\,{\frac {3}{2}};\,-{\frac { \left ( y \left ( x \right ) +x \right ) ^{2}}{ \left ( xy \left ( x \right ) -1 \right ) ^{2}}})}}=0 \right \}$