\[ a \left (y(x)^2-2 x y(x)+1\right )+\left (x^2-1\right ) y'(x)=0 \] ✓ Mathematica : cpu = 0.132398 (sec), leaf count = 158
DSolve[a*(1 - 2*x*y[x] + y[x]^2) + (-1 + x^2)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {\left (x^2-1\right ) \left (c_1 \left (a x \left (x^2-1\right )^{\frac {a}{2}-1} \operatorname {LegendreP}(a-1,x)+\left (x^2-1\right )^{\frac {a}{2}-1} (a \operatorname {LegendreP}(a,x)-a x \operatorname {LegendreP}(a-1,x))\right )+a x \left (x^2-1\right )^{\frac {a}{2}-1} \operatorname {LegendreQ}(a-1,x)+\left (x^2-1\right )^{\frac {a}{2}-1} (a \operatorname {LegendreQ}(a,x)-a x \operatorname {LegendreQ}(a-1,x))\right )}{a \left (\left (x^2-1\right )^{a/2} \operatorname {LegendreQ}(a-1,x)+c_1 \left (x^2-1\right )^{a/2} \operatorname {LegendreP}(a-1,x)\right )}\right \}\right \}\] ✓ Maple : cpu = 0.149 (sec), leaf count = 231
dsolve((x^2-1)*diff(y(x),x)+a*(y(x)^2-2*x*y(x)+1) = 0,y(x))
\[y \left (x \right ) = \frac {8 \left (1+x \right ) \left (\left (a -\frac {1}{2}\right ) x -\frac {a}{2}+\frac {1}{2}\right ) c_{1} \operatorname {HeunC}\left (0, -2 a +1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{1+x}\right )-a \left (1+x \right ) \left (-\frac {x}{2}-\frac {1}{2}\right )^{-2 a +1} \operatorname {HeunC}\left (0, 2 a -1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{1+x}\right )-8 \left (\operatorname {HeunCPrime}\left (0, -2 a +1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{1+x}\right ) c_{1}-\frac {\left (-\frac {x}{2}-\frac {1}{2}\right )^{-2 a +1} \operatorname {HeunCPrime}\left (0, 2 a -1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{1+x}\right )}{4}\right ) \left (x -1\right )}{4 \left (1+x \right ) \left (\operatorname {HeunC}\left (0, -2 a +1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{1+x}\right ) c_{1}-\frac {\left (-\frac {x}{2}-\frac {1}{2}\right )^{-2 a +1} \operatorname {HeunC}\left (0, 2 a -1, 0, 0, a^{2}-a +\frac {1}{2}, \frac {2}{1+x}\right )}{4}\right ) a}\]