\[ \boxed { {x}^{2}{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) -3\, \left ( x-m \right ) x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 2\,{x}^{2}+4\, \left ( n-m \right ) x+m \left ( 2\,m-1 \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,n \left ( 2\,x-2\,m+1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.403551 (sec), leaf count = 43 \[ \left \{\left \{y(x)\to c_2 U(-n,m,x) L_n^{m-1}(x)+c_1 U(-n,m,x)^2+c_3 L_n^{m-1}(x){}^2\right \}\right \} \]
Maple: cpu = 0.094 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {{\sl M}\left (-n,\,m ,\,x\right )} \right ) ^{2}+{\it \_C2}\, \left ( {{\sl U}\left (-n,\,m,\,x \right )} \right ) ^{2}+{\it \_C3}\,{{\sl M}\left (-n,\,m,\,x\right )}{ {\sl U}\left (-n,\,m,\,x\right )} \right \} \]