52.3.1 problem 1

Internal problem ID [8287]
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 : 1
Date solved : Monday, January 27, 2025 at 03:47:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2-1/9)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {BesselJ}\left (\frac {1}{3}, x\right )+c_{2} \operatorname {BesselY}\left (\frac {1}{3}, x\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+(x^2-1/9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}\left (\frac {1}{3},x\right )+c_2 \operatorname {BesselY}\left (\frac {1}{3},x\right ) \]