74.13.10 problem 27

Internal problem ID [16376]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 09:07:19 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(diff(y(t),t$4)+diff(y(t),t$3)=0,y(t), singsol=all)
 

\[ y = c_{1} +c_{2} t +t^{2} c_{3} +c_4 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 26

DSolve[D[y[t],{t,4}]+D[ y[t],{t,3}]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 \left (-e^{-t}\right )+t (c_4 t+c_3)+c_2 \]