\[ \left (4 x (n-m)+m (2 m-1)+2 x^2\right ) y'(x)-2 n (-2 m+2 x+1) y(x)-3 x (x-m) y''(x)+x^2 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.272117 (sec), leaf count = 43
DSolve[-2*n*(1 - 2*m + 2*x)*y[x] + (m*(-1 + 2*m) + 4*(-m + n)*x + 2*x^2)*Derivative[1][y][x] - 3*x*(-m + x)*Derivative[2][y][x] + x^2*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 U(-n,m,x) L_n^{m-1}(x)+c_1 U(-n,m,x)^2+c_3 L_n^{m-1}(x){}^2\right \}\right \}\] ✓ Maple : cpu = 0.104 (sec), leaf count = 39
dsolve(x^2*diff(diff(diff(y(x),x),x),x)-3*(x-m)*x*diff(diff(y(x),x),x)+(2*x^2+4*(n-m)*x+m*(2*m-1))*diff(y(x),x)-2*n*(2*x-2*m+1)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \KummerM \left (-n , m , x\right )^{2}+c_{2} \KummerU \left (-n , m , x\right )^{2}+c_{3} \KummerM \left (-n , m , x\right ) \KummerU \left (-n , m , x\right )\]