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 = 0.532011 (sec), leaf count = 112

DSolve[Derivative[1][y][x] == (1 + x*y[x]^2)^3/(x^4*y[x]*(1 + x + x*y[x]^2)),y[x],x]
 

\[\text {Solve}\left [2 \left (\frac {1}{10} \log \left (2 x^2 y(x)^4+2 x^2 y(x)^2+x^2+4 x y(x)^2+2 x+2\right )-\frac {1}{5} \log \left (x y(x)^2-x+1\right )-\frac {1}{10} \tan ^{-1}\left (2 x y(x)^4+2 x y(x)^2+2 y(x)^2+x+1\right )-\frac {1}{2 x}\right )+\frac {1}{5} \tan ^{-1}\left (2 y(x)^2+1\right )=c_1,y(x)\right ]\]

✓ Maple : cpu = 1.915 (sec), leaf count = 99

dsolve(diff(y(x),x) = (x*y(x)^2+1)^3/x^4/(x*y(x)^2+1+x)/y(x),y(x))
 

\[\frac {2 \ln \left (x y \left (x \right )^{2}-x +1\right ) x -\ln \left (2 y \left (x \right )^{4} x^{2}+\left (2 x^{2}+4 x \right ) y \left (x \right )^{2}+x^{2}+2 x +2\right ) x +\arctan \left (2 x y \left (x \right )^{4}+\left (2+2 x \right ) y \left (x \right )^{2}+1+x \right ) x -\arctan \left (2 y \left (x \right )^{2}+1\right ) x +10 c_{1} x +5}{10 x} = 0\]