76.24.9 problem 11

Internal problem ID [17737]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
Problem number : 11
Date solved : Monday, March 31, 2025 at 04:26:16 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = c_1 +c_2 \sin \left (t \right )+c_3 \cos \left (t \right ) \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.109 (sec). Leaf size: 14

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

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