#### 2.760   ODE No. 760

$y'(x)=\frac {\left (x y(x)^2+1\right )^3}{x^4 y(x) \left (x y(x)^2+x+1\right )}$ Mathematica : cpu = 0.992347 (sec), leaf count = 112

$\text {Solve}\left [2 \left (\frac {1}{10} \log \left (2 x^2 y(x)^4+2 x^2 y(x)^2+x^2+4 x y(x)^2+2 x+2\right )-\frac {1}{5} \log \left (x y(x)^2-x+1\right )-\frac {1}{10} \tan ^{-1}\left (2 x y(x)^4+2 x y(x)^2+2 y(x)^2+x+1\right )-\frac {1}{2 x}\right )+\frac {1}{5} \tan ^{-1}\left (2 y(x)^2+1\right )=c_1,y(x)\right ]$ Maple : cpu = 0.785 (sec), leaf count = 136

$\left \{ -{\frac { \left ( 1+y \left ( x \right ) \right ) \left ( 2\, \left ( y \left ( x \right ) \right ) ^{4}+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) \left ( -1+y \left ( x \right ) \right ) \left ( \ln \left ( 2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}+ \left ( 2\,{x}^{2}+4\,x \right ) \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}+2\,x+2 \right ) x-\arctan \left ( 2\,x \left ( y \left ( x \right ) \right ) ^{4}+ \left ( 2+2\,x \right ) \left ( y \left ( x \right ) \right ) ^{2}+1+x \right ) x-2\,\ln \left ( x \left ( y \left ( x \right ) \right ) ^{2}-x+1 \right ) x+\arctan \left ( 2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) x-5\,{\it \_C1}\,x-5 \right ) }{5\,x \left ( 2\, \left ( y \left ( x \right ) \right ) ^{6}- \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) }}=0 \right \}$