Internal problem ID [12415]
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]]
\[ \boxed {y^{\prime \prime }+\beta y^{\prime }+y \gamma =0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve(diff(y(x),x$2)+beta*diff(y(x),x)+gamma*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {\left (-\beta +\sqrt {\beta ^{2}-4 \gamma }\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {\left (\beta +\sqrt {\beta ^{2}-4 \gamma }\right ) x}{2}} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 47
DSolve[y''[x]+\[Beta]*y'[x]+\[Gamma]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\frac {1}{2} x \left (\sqrt {\beta ^2-4 \gamma }+\beta \right )} \left (c_2 e^{x \sqrt {\beta ^2-4 \gamma }}+c_1\right ) \]