52.3.16 problem 18

Internal problem ID [8302]
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 : 18
Date solved : Monday, January 27, 2025 at 03:48:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(4*x^2*diff(y(x),x$2)+(16*x^2+1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 28

DSolve[4*x^2*D[y[x],{x,2}]+(16*x^2+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} (c_1 \operatorname {BesselJ}(0,2 x)+c_2 \operatorname {BesselY}(0,2 x)) \]