ODE No. 155

\[ \left (x^2-1\right ) y'(x)+y(x)^2-2 x y(x)+1=0 \]

✓ Mathematica : cpu = 0.0950251 (sec), leaf count = 46

DSolve[1 - 2*x*y[x] + y[x]^2 + (-1 + x^2)*Derivative[1][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to -\frac {x \left (1-x^2\right )}{x^2-1}+\frac {1}{\frac {1}{2} \log (1-x)-\frac {1}{2} \log (x+1)+c_1}\right \}\right \}\]

✓ Maple : cpu = 0.105 (sec), leaf count = 14

dsolve((x^2-1)*diff(y(x),x)+y(x)^2-2*x*y(x)+1 = 0,y(x))

\[y \left (x \right ) = x +\frac {1}{c_{1} -\operatorname {arctanh}\left (x \right )}\]