Internal problem ID [8717]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1137.
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 +4 y-\left (x +2\right ) y+l y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 25
dsolve(4*x*diff(diff(y(x),x),x)+4*y(x)-(x+2)*y(x)+l*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \WhittakerM \left (\frac {l}{4}+\frac {1}{2}, \frac {1}{2}, x\right )+c_{2} \WhittakerW \left (\frac {l}{4}+\frac {1}{2}, \frac {1}{2}, x\right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 48
DSolve[4*y[x] + l*y[x] - (2 + x)*y[x] + 4*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-x/2} x \left (c_1 \text {HypergeometricU}\left (\frac {1}{2}-\frac {l}{4},2,x\right )+c_2 \, _1F_1\left (\frac {1}{2}-\frac {l}{4};2;x\right )\right ) \\ \end{align*}