Internal problem ID [11008]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y-1=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(diff(y(t),t$2)+2*diff(y(t),t)+y(t)=1,y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t} c_{2} +{\mathrm e}^{-t} t c_{1} +1 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[y''[t]+2*y'[t]+y[t]==1,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 1+e^{-t} (c_2 t+c_1) \\ \end{align*}