14.21.17 problem 17

Internal problem ID [2726]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.15, Higher order equations. Excercises page 263
Problem number : 17
Date solved : Monday, January 27, 2025 at 06:12:23 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=t +{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(diff(y(t),t$3)+diff(y(t),t$2)+diff(y(t),t)+y(t)=t+exp(-t),y(t), singsol=all)
 

\[ y = \frac {\left (2 c_3 +t +1\right ) {\mathrm e}^{-t}}{2}+\cos \left (t \right ) c_1 +\sin \left (t \right ) c_2 +t -1 \]

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 44

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

\[ y(t)\to c_1 \cos (t)+\frac {1}{2} e^{-t} \left (2 e^t (t-1)+t+2 c_2 e^t \sin (t)+1+2 c_3\right ) \]