7.17.13 problem 13

Internal problem ID [526]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 13
Date solved : Wednesday, February 05, 2025 at 03:42:17 AM
CAS classification : [_Lienard]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

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

\[ y = \frac {c_1 \sin \left (x \right )+c_2 \cos \left (x \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.025 (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]
 

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