Internal problem ID [5869]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
\[ \boxed {x y^{\prime \prime }+y^{\prime }+x y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x*diff(y(x),x$2)+diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (0, x\right )+c_{2} \operatorname {BesselY}\left (0, x\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[x*y''[x]+y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \operatorname {BesselJ}(0,x)+c_2 Y_0(x) \\ \end{align*}