67.5.9 problem Problem 2(d)

Internal problem ID [14024]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 2(d)
Date solved : Monday, March 31, 2025 at 08:22:19 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=5 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(diff(y(t),t),t),t)+3*diff(diff(y(t),t),t)+3*diff(y(t),t)+y(t) = 5; 
dsolve(ode,y(t), singsol=all);
 

\[ y = 5+\left (c_3 \,t^{2}+c_2 t +c_1 \right ) {\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

ode=D[ y[t],{t,3}]+3*D[y[t],{t,2}]+3*D[y[t],t]+y[t]==5; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} \left (5 e^t+t (c_3 t+c_2)+c_1\right ) \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + 3*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)) - 5,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + t \left (C_{2} + C_{3} t\right )\right ) e^{- t} + 5 \]