Internal problem ID [5871]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Bessel]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }+\left (x -\frac {4}{x}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(diff(x*diff(y(x),x),x)+(x-4/x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \BesselJ \left (2, x\right )+c_{2} \BesselY \left (2, x\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 18
DSolve[D[x*y'[x],x]+(x-4/x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 J_2(x)+c_2 Y_2(x) \\ \end{align*}