74.14.1 problem 1

Internal problem ID [16406]
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 : Tuesday, January 28, 2025 at 09:07:35 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

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

dsolve(diff(y(t),t$3)+diff(y(t),t$2)=exp(t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{t}}{2}+{\mathrm e}^{-t} c_{1} +c_{2} t +c_{3} \]

✓ Solution by Mathematica

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

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

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