Internal problem ID [6236]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Bessel]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = c_{1} \BesselJ \left (1, x\right )+c_{2} \BesselY \left (1, x\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 18
DSolve[x^2*y''[x]+x*y'[x]+(x^2-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 J_1(x)+c_2 Y_1(x) \\ \end{align*}