Internal problem ID [5879]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-5 y^{\prime }+x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 21
dsolve(x*diff(y(x),x$2)-5*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{3} \BesselJ \left (3, x\right )+c_{2} x^{3} \BesselY \left (3, x\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 22
DSolve[x*y''[x]-5*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^3 (c_1 J_3(x)+c_2 Y_3(x)) \\ \end{align*}