Internal problem ID [6629]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x y^{\prime \prime }+2 y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} \operatorname {BesselY}\left (1, 4 \sqrt {x}\right )+c_{1} \operatorname {BesselJ}\left (1, 4 \sqrt {x}\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 42
DSolve[x*y''[x]+2*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 \operatorname {BesselJ}\left (1,4 \sqrt {x}\right )-2 i c_2 \operatorname {BesselY}\left (1,4 \sqrt {x}\right )}{2 \sqrt {x}} \]