54.5.11 problem 11 (solved as direct Bessel)

Internal problem ID [8626]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 18. Power series solutions. 18.6. Indicial Equation with Equal Roots. Exercises page 373
Problem number : 11 (solved as direct Bessel)
Date solved : Monday, January 27, 2025 at 04:17:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = c_{1} \operatorname {BesselI}\left (0, x\right )+c_{2} \operatorname {BesselK}\left (0, x\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 26

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

\[ y(x)\to c_1 \operatorname {BesselJ}(0,i x)+c_2 \operatorname {BesselY}(0,-i x) \]