ODE
\[ y(x) \left (\sum _{m=0}^n a(m) x^m\right )+(1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 4.97725 (sec), leaf count = 0 , could not solve
DSolve[Sum[x^m*a[m], {m, 0, n}]*y[x] + (1 - 2*x)*(1 - x)*x*Derivative[1][y][x] + (1 - x)^2*x^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 5.888 (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +{\frac { \left ( 1-2\,x \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{x \left ( 1-x \right ) }}+{\frac {\sum _{m=0}^{n}a \left ( m \right ) {x}^{m}{\it \_Y} \left ( x \right ) }{{x}^{2} \left ( 1-x \right ) ^{2}}} \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]
Mathematica raw input
DSolve[Sum[x^m*a[m], {m, 0, n}]*y[x] + (1 - 2*x)*(1 - x)*x*y'[x] + (1 - x)^2*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[Sum[x^m*a[m], {m, 0, n}]*y[x] + (1 - 2*x)*(1 - x)*x*Derivative[1][y][x] + (1 - x)^2*x^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve(x^2*(1-x)^2*diff(diff(y(x),x),x)+x*(1-x)*(1-2*x)*diff(y(x),x)+sum(a(m)*x^m,m = 0 .. n)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = DESol({diff(diff(_Y(x),x),x)+1/x/(1-x)*(1-2*x)*diff(_Y(x),x)+sum(a(m)*x^m,m = 0 .. n)/x^2/(1-x)^2*_Y(x)},{_Y(x)})