2.779   ODE No. 779

\[ y'(x)=\frac {x^3 y(x)+x^3+x y(x)^2+y(x)^3}{(x-1) x^3} \]

✓ Mathematica : cpu = 0.116017 (sec), leaf count = 57

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

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

✓ Maple : cpu = 0.092 (sec), leaf count = 50

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

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