ODE No. 156

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

✓ Mathematica : cpu = 0.0616234 (sec), leaf count = 21

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

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

✓ Maple : cpu = 0.019 (sec), leaf count = 20

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

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