74.14.9 problem 9

Internal problem ID [16414]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 09:07:40 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y&=-111 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

dsolve(diff(y(t),t$3)+6*diff(y(t),t$2)-14*diff(y(t),t)-104*y(t)=-111*exp(t),y(t), singsol=all)
 

\[ y = \left (c_{1} {\mathrm e}^{9 t}+{\mathrm e}^{6 t}+\sin \left (t \right ) c_{3} +c_{2} \cos \left (t \right )\right ) {\mathrm e}^{-5 t} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 35

DSolve[D[ y[t],{t,3}]+6*D[y[t],{t,2}]-14*D[y[t],t]-104*y[t]==-111*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-5 t} \left (e^{6 t}+c_3 e^{9 t}+c_2 \cos (t)+c_1 \sin (t)\right ) \]