52.3.12 problem 14

Internal problem ID [8298]
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 : 14
Date solved : Monday, January 27, 2025 at 03:48:15 PM
CAS classification : [_Lienard]

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(x*diff(y(x),x$2)+3*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

DSolve[x*D[y[x],{x,2}]+3*D[y[x],x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \operatorname {BesselJ}(1,x)+c_2 \operatorname {BesselY}(1,x)}{x} \]