68.2.6 problem Problem 3.7(f)

Internal problem ID [14151]
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)
Date solved : Tuesday, January 28, 2025 at 06:16:03 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\beta y^{\prime }+\gamma y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(diff(y(x),x$2)+beta*diff(y(x),x)+gamma*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {\left (-\beta +\sqrt {\beta ^{2}-4 \gamma }\right ) x}{2}}+c_{2} {\mathrm e}^{-\frac {\left (\beta +\sqrt {\beta ^{2}-4 \gamma }\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 47

DSolve[D[y[x],{x,2}]+\[Beta]*D[y[x],x]+\[Gamma]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {1}{2} x \left (\sqrt {\beta ^2-4 \gamma }+\beta \right )} \left (c_2 e^{x \sqrt {\beta ^2-4 \gamma }}+c_1\right ) \]