Internal problem ID [11065]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+\alpha ^{2} y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+alpha^2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (\alpha x \right )+c_{2} \cos \left (\alpha x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[y''[x]+a^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (a x)+c_2 \sin (a x) \\ \end{align*}