52.3.6 problem 6

Internal problem ID [8292]
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 : 6
Date solved : Monday, January 27, 2025 at 03:48:02 PM
CAS classification : [_Bessel]

\begin{align*} y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve(diff(x*diff(y(x),x),x)+(x-4/x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {-\operatorname {BesselY}\left (0, x\right ) c_{2} x -\operatorname {BesselJ}\left (0, x\right ) c_{1} x +2 c_{2} \operatorname {BesselY}\left (1, x\right )+2 c_{1} \operatorname {BesselJ}\left (1, x\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 18

DSolve[D[x*D[y[x],x],x]+(x-4/x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}(2,x)+c_2 \operatorname {BesselY}(2,x) \]