54.7.9 problem 10 (as direct Bessel)

Internal problem ID [8657]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 18. Power series solutions. 18.9 Indicial Equation with Difference of Roots a Positive Integer: Logarithmic Case. Exercises page 384
Problem number : 10 (as direct Bessel)
Date solved : Monday, January 27, 2025 at 04:18:31 PM
CAS classification : [_Bessel]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2-1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]+(x^2-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {BesselJ}(1,x)+c_2 \operatorname {BesselY}(1,x) \]