74.13.3 problem 20

Internal problem ID [16290]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 20
Date solved : Thursday, March 13, 2025 at 08:10:04 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 8 y^{\prime \prime \prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=8*diff(diff(diff(y(t),t),t),t)+diff(diff(y(t),t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_{1} +c_{2} t +c_{3} {\mathrm e}^{-\frac {t}{8}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 23

ode=8*D[ y[t],{t,3}]+D[y[t],{t,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 64 c_1 e^{-t/8}+c_3 t+c_2 \]

✓ Sympy. Time used: 0.072 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), (t, 2)) + 8*Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} t + C_{3} e^{- \frac {t}{8}} \]