74.10.6 problem 6

Internal problem ID [16140]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 6
Date solved : Monday, March 31, 2025 at 02:44:44 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

ode:=diff(diff(y(t),t),t)+5*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{t \sqrt {21}}+c_2 \right ) {\mathrm e}^{-\frac {\left (5+\sqrt {21}\right ) t}{2}} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 35

ode=D[y[t],{t,2}]+5*D[y[t],t]+y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-\frac {1}{2} \left (5+\sqrt {21}\right ) t} \left (c_2 e^{\sqrt {21} t}+c_1\right ) \]

✓ Sympy. Time used: 0.217 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + 5*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{\frac {t \left (-5 + \sqrt {21}\right )}{2}} + C_{2} e^{- \frac {t \left (\sqrt {21} + 5\right )}{2}} \]