90.17.4 problem 4

Internal problem ID [25266]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 291
Problem number : 4
Date solved : Thursday, October 02, 2025 at 11:59:27 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \left (c_3 t +c_2 \right ) {\mathrm e}^{-t}+c_1 \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 24

ode=D[y[t],{t,3}]+2*D[y[t],{t,2}]+D[y[t],{t,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_3-e^{-t} (c_2 (t+1)+c_1) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 12

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

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