Internal problem ID [6632]
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]
\[ \boxed {x y^{\prime \prime }-5 y^{\prime }+x y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve(x*diff(y(x),x$2)-5*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\left (c_{1} \left (x^{2}-8\right ) \operatorname {BesselJ}\left (1, x\right )+c_{2} \left (x^{2}-8\right ) \operatorname {BesselY}\left (1, x\right )+4 x \left (c_{1} \operatorname {BesselJ}\left (0, x\right )+c_{2} \operatorname {BesselY}\left (0, x\right )\right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 22
DSolve[x*y''[x]-5*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3 (c_1 \operatorname {BesselJ}(3,x)+c_2 \operatorname {BesselY}(3,x)) \]