Internal problem ID [9438]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1108.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x +\left (x +a +b \right ) y^{\prime }+a y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 26
dsolve(x*diff(diff(y(x),x),x)+(x+a+b)*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \left (\operatorname {KummerU}\left (b , a +b , x\right ) c_{2} +\operatorname {KummerM}\left (b , a +b , x\right ) c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 33
DSolve[a*y[x] + (a + b + x)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} (c_1 \operatorname {HypergeometricU}(b,a+b,x)+c_2 L_{-b}^{a+b-1}(x)) \]