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 : Tuesday, March 04, 2025 at 02:27:17 PM
CAS classification : [[_2nd_order, _missing_x]]

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

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

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

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

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

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

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

✓ Sympy. Time used: 0.245 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*y(t) + 6*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{t \left (-1 + \frac {\sqrt {3}}{3}\right )} + C_{2} e^{- t \left (\frac {\sqrt {3}}{3} + 1\right )} \]