52.3.14 problem 16

Internal problem ID [8300]
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
Date solved : Monday, January 27, 2025 at 03:48:17 PM
CAS classification : [_Lienard]

\begin{align*} x y^{\prime \prime }-5 y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 42

dsolve(x*diff(y(x),x$2)-5*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
 

\[ y = -x \left (c_{1} \left (x^{2}-8\right ) \operatorname {BesselJ}\left (1, x\right )+c_{2} \left (x^{2}-8\right ) \operatorname {BesselY}\left (1, x\right )+4 x \left (c_{1} \operatorname {BesselJ}\left (0, x\right )+c_{2} \operatorname {BesselY}\left (0, x\right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

DSolve[x*D[y[x],{x,2}]-5*D[y[x],x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 (c_1 \operatorname {BesselJ}(3,x)+c_2 \operatorname {BesselY}(3,x)) \]