4.46.27 \(x^n y^{(2 n)}(x)=y(x)\)

ODE
\[ x^n y^{(2 n)}(x)=y(x) \] ODE Classification

(ODEtools/info) missing specification of intermediate function

Book solution method
TO DO

Mathematica
cpu = 0.00486123 (sec), leaf count = 0 , could not solve

DSolve[x^n*Derivative[2*n][y][x] == 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[x^n*Derivative[2*n][y][x] == y[x],y[x],x]

Mathematica raw output

DSolve[x^n*Derivative[2*n][y][x] == y[x], y[x], x]

Maple raw input

dsolve(diff(y(x),[`$`(x,2*n)])*x^n = y(x), y(x),'implicit')

Maple raw output

unable to handle ODEs of undefined differential order