90.18.5 problem 9

Internal problem ID [25277]
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 299
Problem number : 9
Date solved : Thursday, October 02, 2025 at 11:59:32 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = -{\mathrm e}^{-t} c_2 +\frac {\left (t +2 c_1 -1\right ) {\mathrm e}^{t}}{2}+c_3 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 32

ode=D[y[t],{t,3}]-D[y[t],{t,1}]==Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^t \left (\frac {t}{2}-\frac {3}{4}+c_1\right )-c_2 e^{-t}+c_3 \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 17

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

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