ODE
\[ y(x) \left (\sum _{m=0}^n a(m) x^{2 m}\right )+\left (1-x^2\right ) y''(x)-x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 1.19961 (sec), leaf count = 0 , could not solve
DSolve[Sum[x^(2*m)*a[m], {m, 0, n}]*y[x] - x*Derivative[1][y][x] + (1 - x^2)*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 9.066 (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) -{\frac {x{\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{-{x}^{2}+1}}+{\frac {\sum _{m=0}^{n}a \left ( m \right ) {x}^{2\,m}{\it \_Y} \left ( x \right ) }{-{x}^{2}+1}} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]
Mathematica raw input
DSolve[Sum[x^(2*m)*a[m], {m, 0, n}]*y[x] - x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[Sum[x^(2*m)*a[m], {m, 0, n}]*y[x] - x*Derivative[1][y][x] + (1 - x^2)*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve((-x^2+1)*diff(diff(y(x),x),x)-x*diff(y(x),x)+sum(a(m)*x^(2*m),m = 0 .. n)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = DESol({diff(diff(_Y(x),x),x)-x/(-x^2+1)*diff(_Y(x),x)+sum(a(m)*x^(2*m),m = 0 .. n)/(-x^2+1)*_Y(x)},{_Y(x)})