\[ 3 \left (x^2-4\right ) y'(x)+y(x)^2-x y(x)-3=0 \] ✓ Mathematica : cpu = 0.204183 (sec), leaf count = 234
DSolve[-3 - x*y[x] + y[x]^2 + 3*(-4 + x^2)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {3 \left (x^2-4\right ) \left (c_1 \left (\frac {x P_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )}{6 \left (x^2-4\right )^{11/12}}+\frac {\sqrt [12]{x^2-4} \left (\frac {1}{2} P_{\frac {5}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )-\frac {5}{12} x P_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )\right )}{2 \left (\frac {x^2}{4}-1\right )}\right )+\frac {x Q_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )}{6 \left (x^2-4\right )^{11/12}}+\frac {\sqrt [12]{x^2-4} \left (\frac {1}{2} Q_{\frac {5}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )-\frac {5}{12} x Q_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )\right )}{2 \left (\frac {x^2}{4}-1\right )}\right )}{\sqrt [12]{x^2-4} Q_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )+c_1 \sqrt [12]{x^2-4} P_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )}\right \}\right \}\] ✓ Maple : cpu = 0.171 (sec), leaf count = 140
dsolve(3*(x^2-4)*diff(y(x),x)+y(x)^2-x*y(x)-3 = 0,y(x))
\[y \left (x \right ) = -\frac {3 \left (\HeunC \left (0, \frac {4}{3}, -\frac {1}{3}, 0, \frac {25}{36}, \frac {4}{x +2}\right ) c_{1}-\frac {\left (-\frac {x}{4}-\frac {1}{2}\right )^{\frac {4}{3}} \HeunC \left (0, -\frac {4}{3}, -\frac {1}{3}, 0, \frac {25}{36}, \frac {4}{x +2}\right )}{3}\right ) \left (x +2\right )}{4 c_{1} \left (x -\frac {5}{4}\right ) \left (x +2\right ) \HeunC \left (0, \frac {4}{3}, -\frac {1}{3}, 0, \frac {25}{36}, \frac {4}{x +2}\right )-\left (-\frac {x}{4}-\frac {1}{2}\right )^{\frac {4}{3}} \left (x +2\right ) \HeunC \left (0, -\frac {4}{3}, -\frac {1}{3}, 0, \frac {25}{36}, \frac {4}{x +2}\right )+12 \left (\HeunCPrime \left (0, \frac {4}{3}, -\frac {1}{3}, 0, \frac {25}{36}, \frac {4}{x +2}\right ) c_{1}-\frac {\left (-\frac {x}{4}-\frac {1}{2}\right )^{\frac {4}{3}} \HeunCPrime \left (0, -\frac {4}{3}, -\frac {1}{3}, 0, \frac {25}{36}, \frac {4}{x +2}\right )}{3}\right ) \left (x -2\right )}\]