Internal problem ID [11067]
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(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+\beta y^{\prime }+\gamma y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(y(x),x$2)+beta*diff(y(x),x)+gamma*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\left (-\frac {\beta }{2}+\frac {\sqrt {\beta ^{2}-4 \gamma }}{2}\right ) x}+c_{2} {\mathrm e}^{\left (-\frac {\beta }{2}-\frac {\sqrt {\beta ^{2}-4 \gamma }}{2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 47
DSolve[y''[x]+\[Beta]*y'[x]+\[Gamma]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {1}{2} x \left (\sqrt {\beta ^2-4 \gamma }+\beta \right )} \left (c_2 e^{x \sqrt {\beta ^2-4 \gamma }}+c_1\right ) \\ \end{align*}