Internal problem ID [5878]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }+x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 17
dsolve(x*diff(y(x),x$2)-diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \BesselJ \left (1, x\right )+c_{2} x \BesselY \left (1, x\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[x*y''[x]-y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x J_1(x)+c_2 x Y_1(x) \\ \end{align*}