7.7.4 problem 4

Internal problem ID [2367]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2, linear equations with constant coefficients. Page 138
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 05:34:56 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 18

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

\begin{align*} y(t)&\to e^{-t} (c_2 t+c_1) \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 10

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

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