59.1.785 problem 807

Internal problem ID [9957]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 807
Date solved : Monday, January 27, 2025 at 06:16:09 PM
CAS classification : [_Lienard]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\sin \left (x \right ) c_{1} +\cos \left (x \right ) c_{2}}{x} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 37

DSolve[x*D[y[x],{x,2}]+2*D[y[x],x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 c_1 e^{-i x}-i c_2 e^{i x}}{2 x} \]