Internal problem ID [6987]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 256.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+2 y^{\prime }+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \relax (x )}{x}+\frac {c_{2} \cos \relax (x )}{x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 37
DSolve[x*y''[x]+2*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 c_1 e^{-i x}-i c_2 e^{i x}}{2 x} \\ \end{align*}