74.14.10 problem 10

Internal problem ID [16415]
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 : 10
Date solved : Tuesday, January 28, 2025 at 09:07:40 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y&=153 \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 33

dsolve(diff(y(t),t$4)-10*diff(y(t),t$3)+38*diff(y(t),t$2)-64*diff(y(t),t)+40*y(t)=153*exp(-t),y(t), singsol=all)
 

\[ y = \left (c_{2} t +c_{1} \right ) {\mathrm e}^{2 t}+\left (\cos \left (t \right ) c_{3} +\sin \left (t \right ) c_4 \right ) {\mathrm e}^{3 t}+{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 48

DSolve[D[y[t],{t,4}]-10*D[ y[t],{t,3}]+38*D[y[t],{t,2}]-64*D[y[t],t]+40*y[t]==153*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t}+c_3 e^{2 t}+c_4 e^{2 t} t+c_2 e^{3 t} \cos (t)+c_1 e^{3 t} \sin (t) \]