Internal problem ID [8687]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1107.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x +\left (x +b \right ) y^{\prime }+a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 33
dsolve(x*diff(diff(y(x),x),x)+(x+b)*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-x} \KummerM \left (-a +b , b , x\right )+c_{2} {\mathrm e}^{-x} \KummerU \left (-a +b , b , x\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 36
DSolve[a*y[x] + (b + x)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (c_1 \text {HypergeometricU}(b-a,b,x)+c_2 L_{a-b}^{b-1}(x)) \\ \end{align*}