52.3.7 problem 7

Internal problem ID [8293]
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 : 7
Date solved : Monday, January 27, 2025 at 03:48:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 44

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(9*x^2-4)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {-3 \operatorname {BesselJ}\left (0, 3 x \right ) c_{1} x -3 \operatorname {BesselY}\left (0, 3 x \right ) c_{2} x +2 \operatorname {BesselJ}\left (1, 3 x \right ) c_{1} +2 \operatorname {BesselY}\left (1, 3 x \right ) c_{2}}{3 x} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+(9*x^2-4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}(2,3 x)+c_2 \operatorname {BesselY}(2,3 x) \]