Internal problem ID [6624]
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]
\[ \boxed {x y^{\prime \prime }+y^{\prime }+\left (x -\frac {4}{x}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(x*diff(y(x),x),x)+(x-4/x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\operatorname {BesselJ}\left (0, x\right ) c_{1} x -\operatorname {BesselY}\left (0, x\right ) c_{2} x +2 c_{1} \operatorname {BesselJ}\left (1, x\right )+2 c_{2} \operatorname {BesselY}\left (1, x\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 18
DSolve[D[x*y'[x],x]+(x-4/x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {BesselJ}(2,x)+c_2 \operatorname {BesselY}(2,x) \]