74.14.21 problem 21

Internal problem ID [16426]
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 : 21
Date solved : Tuesday, January 28, 2025 at 09:07:50 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y&={\mathrm e}^{-3 t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 30

dsolve(diff(y(t),t$3)+3*diff(y(t),t$2)-10*diff(y(t),t)-24*y(t)=exp(-3*t),y(t), singsol=all)
 

\[ y = \frac {\left (6 c_{3} {\mathrm e}^{7 t}+6 c_{2} {\mathrm e}^{2 t}+{\mathrm e}^{t}+6 c_{1} \right ) {\mathrm e}^{-4 t}}{6} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 40

DSolve[D[ y[t],{t,3}]+3*D[y[t],{t,2}]-10*D[y[t],t]-24*y[t]==Exp[-3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{6} e^{-4 t} \left (e^t+6 c_2 e^{2 t}+6 c_3 e^{7 t}+6 c_1\right ) \]