14.7.3 problem 3

Internal problem ID [2547]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2. Linear equations with constant coefficients. Excercises page 140
Problem number : 3
Date solved : Monday, January 27, 2025 at 06:00:00 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(diff(y(t),t$2)-3*diff(y(t),t)+y(t)=0,y(t), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{\frac {\left (3+\sqrt {5}\right ) t}{2}}+c_2 \,{\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) t}{2}} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 35

DSolve[D[y[t],{t,2}]-3*D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-\frac {1}{2} \left (\sqrt {5}-3\right ) t} \left (c_2 e^{\sqrt {5} t}+c_1\right ) \]