14.7.4 problem 4

Internal problem ID [2548]
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 : 4
Date solved : Monday, January 27, 2025 at 06:00:02 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

dsolve(3*diff(y(t),t$2)+6*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 37

DSolve[3*D[y[t],{t,2}]+6*D[y[t],t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

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