67.5.9 problem Problem 2(d)

Internal problem ID [14095]
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 : Tuesday, January 28, 2025 at 06:14:22 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve(diff(y(t),t$3)+3*diff(y(t),t$2)+3*diff(y(t),t)+y(t)=5,y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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