67.5.6 problem Problem 2(a)

Internal problem ID [14021]
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(a)
Date solved : Monday, March 31, 2025 at 08:22:15 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=1 \end{align*}

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

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+y(t) = 1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = 1+\left (c_1 t +c_2 \right ) {\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.158 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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