90.17.10 problem 10

Internal problem ID [25272]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 291
Problem number : 10
Date solved : Thursday, October 02, 2025 at 11:59:29 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 17

ode:=diff(diff(diff(y(t),t),t),t)+diff(diff(y(t),t),t)-diff(y(t),t)-y(t) = 0; 
ic:=[y(0) = 1, D(y)(0) = 4, (D@@2)(y)(0) = -1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{t}+{\mathrm e}^{-t} \left (t -1\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 21

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

\begin{align*} y(t)&\to e^{-t} \left (t+2 e^{2 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 14

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

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