74.14.1 problem 1

Internal problem ID [16335]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 1
Date solved : Monday, March 31, 2025 at 02:50:35 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 27

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

\[ y(t)\to \frac {e^t}{2}+c_1 e^{-t}+c_3 t+c_2 \]

✓ Sympy. Time used: 0.081 (sec). Leaf size: 17

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

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