4.46.31 \((a-x)^n (b-x)^n y^{(n)}(x)=c y(x)\)

ODE
\[ (a-x)^n (b-x)^n y^{(n)}(x)=c y(x) \] ODE Classification

(ODEtools/info) missing specification of intermediate function

Book solution method
TO DO

Mathematica
cpu = 0.00554888 (sec), leaf count = 0 , could not solve

DSolve[(a - x)^n*(b - x)^n*Derivative[n][y][x] == c*y[x], y[x], x]

Maple
cpu = 0.034 (sec), leaf count = 0 , exception

unable to handle ODEs of undefined differential order

Mathematica raw input

DSolve[(a - x)^n*(b - x)^n*Derivative[n][y][x] == c*y[x],y[x],x]

Mathematica raw output

DSolve[(a - x)^n*(b - x)^n*Derivative[n][y][x] == c*y[x], y[x], x]

Maple raw input

dsolve(diff(y(x),[`$`(x,n)])*(a-x)^n*(b-x)^n = c*y(x), y(x),'implicit')

Maple raw output

unable to handle ODEs of undefined differential order