68.14.5 problem 5

Internal problem ID [17697]
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 : Thursday, October 02, 2025 at 02:27:08 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+9*diff(diff(y(t),t),t) = 9*exp(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {\cos \left (3 t \right ) c_1}{9}-\frac {\sin \left (3 t \right ) c_2}{9}+\frac {{\mathrm e}^{3 t}}{18}+c_3 t +c_4 \]

✓ Mathematica. Time used: 60.026 (sec). Leaf size: 54

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

\begin{align*} 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 \end{align*}

✓ Sympy. Time used: 0.049 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-9*exp(3*t) + 9*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} t + C_{3} \sin {\left (3 t \right )} + C_{4} \cos {\left (3 t \right )} + \frac {e^{3 t}}{18} \]