Internal problem ID [11011]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y-5=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(t),t$3)+3*diff(y(t),t$2)+3*diff(y(t),t)+y(t)=5,y(t), singsol=all)
\[ y \left (t \right ) = 5+c_{1} {\mathrm e}^{-t}+c_{2} t^{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{-t} t \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 25
DSolve[y'''[t]+3*y''[t]+3*y'[t]+y[t]==5,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 5+e^{-t} (t (c_3 t+c_2)+c_1) \\ \end{align*}