ODE No. 888

\[ y'(x)=\frac {x^4 y(x)^3-5 x^3 y(x)^2+6 x^2 y(x)-2 x y(x)-2 x+1}{x^2 \left (x^2 y(x)-x+1\right )} \] Mathematica : cpu = 0.161241 (sec), leaf count = 78

DSolve[Derivative[1][y][x] == (1 - 2*x - 2*x*y[x] + 6*x^2*y[x] - 5*x^3*y[x]^2 + x^4*y[x]^3)/(x^2*(1 - x + x^2*y[x])),y[x],x]
 

\[\left \{\left \{y(x)\to \frac {x-1}{x^2}+\frac {1}{x^4 \left (\frac {1}{x^2}-\frac {1}{x^2 \sqrt {\frac {2}{x}+c_1}}\right )}\right \},\left \{y(x)\to \frac {x-1}{x^2}+\frac {1}{x^4 \left (\frac {1}{x^2}+\frac {1}{x^2 \sqrt {\frac {2}{x}+c_1}}\right )}\right \}\right \}\] Maple : cpu = 0.05 (sec), leaf count = 79

dsolve(diff(y(x),x) = 1/x^2*(6*x^2*y(x)-2*x+1-5*x^3*y(x)^2-2*x*y(x)+y(x)^3*x^4)/(x^2*y(x)-x+1),y(x))
 

\[y \left (x \right ) = \frac {\sqrt {\frac {x c_{1}+2}{x}}\, x -x +1}{x^{2} \left (\sqrt {\frac {x c_{1}+2}{x}}-1\right )}\]