Internal problem ID [5877]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+3 y^{\prime }+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(x*diff(y(x),x$2)+3*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \BesselJ \left (1, x\right )}{x}+\frac {c_{2} \BesselY \left (1, x\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 22
DSolve[x*y''[x]+3*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 J_1(x)+c_2 Y_1(x)}{x} \\ \end{align*}