90.29.8 problem 25

Internal problem ID [25440]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 6. Discontinuous Functions and the Laplace Transform. Exercises at page 449
Problem number : 25
Date solved : Friday, October 03, 2025 at 12:01:33 AM
CAS classification : [[_3rd_order, _missing_x]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 10

ode:=diff(diff(diff(y(t),t),t),t)+diff(y(t),t) = 0; 
ic:=[y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 4]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = -4 \cos \left (t \right )+5 \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 11

ode=D[y[t],{t,3}]+D[y[t],t]==0; 
ic={y[0]==1,Derivative[1][y][0] ==0,Derivative[2][y][0] ==4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 5-4 \cos (t) \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) + Derivative(y(t), (t, 3)),0) 
ics = {y(0): 1, Subs(Derivative(y(t), t), t, 0): 0, Subs(Derivative(y(t), (t, 2)), t, 0): 4} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 5 - 4 \cos {\left (t \right )} \]