ODE
\[ y(x) \left (4 k x-4 p^2-x^2+1\right )+4 x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.167218 (sec), leaf count = 20
\[\{\{y(x)\to c_1 M_{k,p}(x)+c_2 W_{k,p}(x)\}\}\]
Maple ✓
cpu = 0.315 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} \WhittakerM \left (k , p , x\right )+\textit {\_C2} \WhittakerW \left (k , p , x\right )]\] Mathematica raw input
DSolve[(1 - 4*p^2 + 4*k*x - x^2)*y[x] + 4*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*WhittakerM[k, p, x] + C[2]*WhittakerW[k, p, x]}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)+(4*k*x-4*p^2-x^2+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*WhittakerM(k,p,x)+_C2*WhittakerW(k,p,x)]