14.8.3 problem 3

Internal problem ID [2558]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2.1 Linear equations with constant coefficients (complex roots). Excercises page 144
Problem number : 3
Date solved : Sunday, March 30, 2025 at 12:10:08 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 34

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

\[ y(t)\to e^{-t} \left (c_2 \cos \left (\sqrt {2} t\right )+c_1 \sin \left (\sqrt {2} t\right )\right ) \]

✓ Sympy. Time used: 0.160 (sec). Leaf size: 26

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

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