\[ 2 \left (x^2-1\right ) x y'(x)+2 \left (x^2-1\right ) y(x)^2-\left (3 x^2-5\right ) y(x)+x^2-3=0 \] ✓ Mathematica : cpu = 0.160648 (sec), leaf count = 49
DSolve[-3 + x^2 - (-5 + 3*x^2)*y[x] + 2*(-1 + x^2)*y[x]^2 + 2*x*(-1 + x^2)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to 1+\frac {\sqrt {x}}{\sqrt {1-x^2} \left (2 \sqrt {x} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};x^2\right )+c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.109 (sec), leaf count = 61
dsolve(2*x*(x^2-1)*diff(y(x),x)+2*(x^2-1)*y(x)^2-(3*x^2-5)*y(x)+x^2-3 = 0,y(x))
\[y \left (x \right ) = 1-\frac {2 \sqrt {x}}{\sqrt {1+x}\, \sqrt {x -1}\, \left (c_{1}-\frac {2 \EllipticF \left (\sqrt {1+x}, \frac {\sqrt {2}}{2}\right ) \sqrt {-x}\, \sqrt {2}\, \sqrt {1-x}}{\sqrt {x -1}\, \sqrt {x}}\right )}\]