74.13.1 problem 17

Internal problem ID [16288]
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 : 17
Date solved : Thursday, March 13, 2025 at 08:10:02 AM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {1}{2} c_{1} t^{2}+c_{2} t +c_{3} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 17

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

\[ y(t)\to t (c_3 t+c_2)+c_1 \]

✓ Sympy. Time used: 0.043 (sec). Leaf size: 12

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

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