74.14.3 problem 3

Internal problem ID [16408]
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 : 3
Date solved : Tuesday, January 28, 2025 at 09:07:36 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

dsolve(diff(y(t),t$5)-diff(y(t),t$4)=1,y(t), singsol=all)
 

\[ y = -\frac {t^{4}}{24}+\frac {c_{2} t^{3}}{6}+\frac {t^{2} c_{3}}{2}+c_{1} {\mathrm e}^{t}+t c_4 +c_5 \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 37

DSolve[D[ y[t],{t,5}]-D[y[t],{t,4}]==1,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {t^4}{24}+c_5 t^3+c_4 t^2+c_3 t+c_1 e^t+c_2 \]