74.14.5 problem 5

Internal problem ID [16410]
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 : 5
Date solved : Tuesday, January 28, 2025 at 09:07:37 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+9 y^{\prime \prime }&=9 \,{\mathrm e}^{3 t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(diff(y(t),t$4)+9*diff(y(t),t$2)=9*exp(3*t),y(t), singsol=all)
 

\[ y = -\frac {\cos \left (3 t \right ) c_{1}}{9}-\frac {\sin \left (3 t \right ) c_{2}}{9}+\frac {{\mathrm e}^{3 t}}{18}+c_{3} t +c_4 \]

✓ Solution by Mathematica

Time used: 60.040 (sec). Leaf size: 54

DSolve[D[y[t],{t,4}]+9*D[y[t],{t,2}]==9*Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t\int _1^{K[2]}\left (c_1 \cos (3 K[1])+\frac {1}{2} e^{3 K[1]}+c_2 \sin (3 K[1])\right )dK[1]dK[2]+c_4 t+c_3 \]