Internal problem ID [12414]
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).
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: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-alpha^2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\alpha x}+c_{2} {\mathrm e}^{\alpha x} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 23
DSolve[y''[x]-a^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{a x}+c_2 e^{-a x} \]