52.3.11 problem 13

Internal problem ID [8297]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL FUNCTIONS. EXERCISES 6.4. Page 267
Problem number : 13
Date solved : Monday, January 27, 2025 at 03:48:14 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 27

dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} \operatorname {BesselY}\left (1, 4 \sqrt {x}\right )+c_{1} \operatorname {BesselJ}\left (1, 4 \sqrt {x}\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 42

DSolve[x*D[y[x],{x,2}]+2*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \operatorname {BesselJ}\left (1,4 \sqrt {x}\right )-2 i c_2 \operatorname {BesselY}\left (1,4 \sqrt {x}\right )}{2 \sqrt {x}} \]