Internal problem ID [6631]
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]
\[ \boxed {x y^{\prime \prime }-y^{\prime }+y x=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(x*diff(y(x),x$2)-diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \operatorname {BesselJ}\left (1, x\right )+c_{2} x \operatorname {BesselY}\left (1, x\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 20
DSolve[x*y''[x]-y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (c_1 \operatorname {BesselJ}(1,x)+c_2 \operatorname {BesselY}(1,x)) \]