52.3.9 problem 9

Internal problem ID [8295]
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 : 9
Date solved : Monday, January 27, 2025 at 03:48:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(25*x^2-4/9)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {BesselJ}\left (\frac {2}{3}, 5 x \right )+c_{2} \operatorname {BesselY}\left (\frac {2}{3}, 5 x \right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+(25*x^2-4/9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}\left (\frac {2}{3},5 x\right )+c_2 \operatorname {BesselY}\left (\frac {2}{3},5 x\right ) \]