\[ \left (x^2-1\right ) y''(x)+\left (x^2+1\right ) y(x)+4 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0226523 (sec), leaf count = 45
DSolve[(1 + x^2)*y[x] + 4*x*Derivative[1][y][x] + (-1 + x^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 e^{-i x}}{x^2-1}-\frac {i c_2 e^{i x}}{2 \left (x^2-1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.036 (sec), leaf count = 21
dsolve((x^2-1)*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+(x^2+1)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {\sin \left (x \right ) c_{1}+c_{2} \cos \left (x \right )}{x^{2}-1}\]