Internal problem ID [8853]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1273.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime } x^{2}-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(4*x^2*diff(diff(y(x),x),x)-(-4*k*x+4*m^2+x^2-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \WhittakerM \left (k , m , x\right )+c_{2} \WhittakerW \left (k , m , x\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 20
DSolve[(1 - 4*m^2 + 4*k*x - x^2)*y[x] + 4*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 M_{k,m}(x)+c_2 W_{k,m}(x) \\ \end{align*}