Internal problem ID [9431]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1101.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x +2 y^{\prime }+y a x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(x*diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x)*a*x=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \sinh \left (\sqrt {-a}\, x \right )+c_{2} \cosh \left (\sqrt {-a}\, x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 52
DSolve[a*x*y[x] + 2*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 c_1 e^{-i \sqrt {a} x}-\frac {i c_2 e^{i \sqrt {a} x}}{\sqrt {a}}}{2 x} \]