\[ a x y(x)^2+\left (x^2-1\right ) y'(x)+x y(x)=0 \] ✓ Mathematica : cpu = 0.153612 (sec), leaf count = 31
DSolve[x*y[x] + a*x*y[x]^2 + (-1 + x^2)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {e^{c_1}}{-\sqrt {x^2-1}+a e^{c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.017 (sec), leaf count = 22
dsolve((x^2-1)*diff(y(x),x)+a*x*y(x)^2+x*y(x) = 0,y(x))
\[y \left (x \right ) = \frac {1}{\sqrt {x -1}\, \sqrt {1+x}\, c_{1}-a}\]