\[ y(x) \left (2 x (2 l-m+1)-m^2-x^2+1\right )+4 x^2 y''(x)+4 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0252521 (sec), leaf count = 120
DSolve[(1 - m^2 + 2*(1 + 2*l - m)*x - x^2)*y[x] + 4*x*Derivative[1][y][x] + 4*x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} \left (\sqrt {m^2-1} \log (x)-x\right )} U\left (\frac {1}{2} \left (-2 l+m+\sqrt {m^2-1}\right ),\sqrt {m^2-1}+1,x\right )+c_2 e^{\frac {1}{2} \left (\sqrt {m^2-1} \log (x)-x\right )} L_{\frac {1}{2} \left (2 l-m-\sqrt {m^2-1}\right )}^{\sqrt {m^2-1}}(x)\right \}\right \}\] ✓ Maple : cpu = 0.139 (sec), leaf count = 53
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+(-x^2+2*(1-m+2*l)*x-m^2+1)*y(x)=0,y(x))
\[y \left (x \right ) = \frac {c_{2} \WhittakerW \left (l -\frac {m}{2}+\frac {1}{2}, \frac {\sqrt {m -1}\, \sqrt {m +1}}{2}, x\right )+c_{1} \WhittakerM \left (l -\frac {m}{2}+\frac {1}{2}, \frac {\sqrt {m -1}\, \sqrt {m +1}}{2}, x\right )}{\sqrt {x}}\]