90.16.1 problem 1

Internal problem ID [25259]
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 283
Problem number : 1
Date solved : Thursday, October 02, 2025 at 11:59:25 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&={\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(diff(y(t),t),t),t)-3*diff(y(t),t) = exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\sqrt {3}\, {\mathrm e}^{\sqrt {3}\, t} c_2}{3}-\frac {\sqrt {3}\, {\mathrm e}^{-\sqrt {3}\, t} c_1}{3}-\frac {{\mathrm e}^{t}}{2}+c_3 \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 51

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

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

✓ Sympy. Time used: 0.127 (sec). Leaf size: 29

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

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