ODE
\[ y(x) \left (\sum _{m=0}^n a(m) x^m\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 40.315 (sec), leaf count = 0 , could not solve
DSolve[Sum[x^m*a[m], {m, 0, n}]*y[x] - 2*x*(1 - x^2)*Derivative[1][y][x] + (1 - x^2)^2*Derivative[2][y][x] == 0, y[x], x]
Maple ✗
cpu = 21.505 (sec), leaf count = 0 , result contains DESol or ODESolStruc
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Mathematica raw input
DSolve[Sum[x^m*a[m], {m, 0, n}]*y[x] - 2*x*(1 - x^2)*y'[x] + (1 - x^2)^2*y''[x] == 0,y[x],x]
Mathematica raw output
DSolve[Sum[x^m*a[m], {m, 0, n}]*y[x] - 2*x*(1 - x^2)*Derivative[1][y][x] + (1 - x^2)^2*Derivative[2][y][x] == 0, y[x], x]
Maple raw input
dsolve((-x^2+1)^2*diff(diff(y(x),x),x)-2*x*(-x^2+1)*diff(y(x),x)+sum(a(m)*x^m,m = 0 .. n)*y(x) = 0, y(x))
Maple raw output
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