77.1.143 problem thm 20 (page 244)

Internal problem ID [18033]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : thm 20 (page 244)
Date solved : Tuesday, January 28, 2025 at 11:23:09 AM
CAS classification : [_Lienard]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+2/x*diff(y(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: 0.025 (sec). Leaf size: 37

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

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