68.10.12 problem 12

Internal problem ID [17504]
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 : 12
Date solved : Thursday, October 02, 2025 at 02:24:51 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+21 y^{\prime }+5 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=4*diff(diff(y(t),t),t)+21*diff(y(t),t)+5*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {t}{4}}+c_2 \,{\mathrm e}^{-5 t} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 35

ode=D[y[t],{t,2}]+21*D[y[t],t]+5*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-\frac {1}{2} \left (21+\sqrt {421}\right ) t} \left (c_2 e^{\sqrt {421} t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*y(t) + 21*Derivative(y(t), t) + 4*Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 5 t} + C_{2} e^{- \frac {t}{4}} \]