70.24.9 problem 11

Internal problem ID [19094]
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 : Thursday, October 02, 2025 at 03:37:56 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: 43.981 (sec). Leaf size: 94

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

\begin{align*} y(t)&\to \int _1^t(c_1 \cos (K[1])+c_2 \sin (K[1]))dK[1]+c_3\\ y(t)&\to c_2 \left (-\cos \left (2 \pi \text {frac}\left (\frac {t-1}{2 \pi }\right )+1\right )\right )+c_3+c_2 \cos (1)\\ y(t)&\to c_1 \sin \left (2 \pi \text {frac}\left (\frac {t-1}{2 \pi }\right )+1\right )+c_3-c_1 \sin (1) \end{align*}

✓ Sympy. Time used: 0.058 (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)
 

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