67.5.6 problem Problem 2(a)

Internal problem ID [14092]
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 : Tuesday, January 28, 2025 at 06:14:12 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(y(t),t$2)+2*diff(y(t),t)+y(t)=1,y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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