Internal problem ID [9431]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1096.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x +y^{\prime }+y \left (x +a \right )=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 43
dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x)+(x+a)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-i x} \operatorname {KummerM}\left (\frac {1}{2}+\frac {i a}{2}, 1, 2 i x \right )+c_{2} {\mathrm e}^{-i x} \operatorname {KummerU}\left (\frac {1}{2}+\frac {i a}{2}, 1, 2 i x \right ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 55
DSolve[(a + x)*y[x] + y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-i x} \left (c_1 \operatorname {HypergeometricU}\left (\frac {i a}{2}+\frac {1}{2},1,2 i x\right )+c_2 \operatorname {LaguerreL}\left (-\frac {1}{2} i (a-i),2 i x\right )\right ) \]