68.2.5 problem Problem 3.7(e)

Internal problem ID [14150]
Book : Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section : Chapter 3 Bessel functions. Problems page 89
Problem number : Problem 3.7(e)
Date solved : Tuesday, January 28, 2025 at 06:15:59 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-\alpha ^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

\[ y = c_{1} {\mathrm e}^{-\alpha x}+c_{2} {\mathrm e}^{\alpha x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 23

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

\[ y(x)\to c_1 e^{a x}+c_2 e^{-a x} \]