68.2.4 problem Problem 3.7(d)

Internal problem ID [14149]
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(d)
Date solved : Tuesday, January 28, 2025 at 06:15:57 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y = c_{1} \sin \left (\alpha x \right )+c_{2} \cos \left (\alpha x \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

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

\[ y(x)\to c_1 \cos (a x)+c_2 \sin (a x) \]