Internal problem ID [8711]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1131.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.375 (sec). Leaf size: 35
dsolve(2*x*diff(diff(y(x),x),x)-(x-1)*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \KummerM \left (-a +\frac {1}{2}, \frac {3}{2}, \frac {x}{2}\right ) \sqrt {x}+c_{2} \KummerU \left (-a +\frac {1}{2}, \frac {3}{2}, \frac {x}{2}\right ) \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 48
DSolve[a*y[x] - (-1 + x)*y'[x] + 2*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} \left (c_1 \text {HypergeometricU}\left (\frac {1}{2}-a,\frac {3}{2},\frac {x}{2}\right )+c_2 L_{a-\frac {1}{2}}^{\frac {1}{2}}\left (\frac {x}{2}\right )\right ) \\ \end{align*}