74.14.24 problem 24

Internal problem ID [16429]
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 : 24
Date solved : Tuesday, January 28, 2025 at 09:07:51 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 34

dsolve(diff(y(t),t$6)+diff(y(t),t$4)=-24,y(t), singsol=all)
 

\[ y = \frac {c_{3} t^{3}}{6}-t^{4}+\frac {c_4 \,t^{2}}{2}+\cos \left (t \right ) c_{1} +c_{2} \sin \left (t \right )+c_5 t +c_6 \]

✓ Solution by Mathematica

Time used: 60.028 (sec). Leaf size: 67

DSolve[D[ y[t],{t,6}]+D[y[t],{t,4}]==-24,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t\int _1^{K[4]}\int _1^{K[3]}\int _1^{K[2]}(c_1 \cos (K[1])+c_2 \sin (K[1])-24)dK[1]dK[2]dK[3]dK[4]+t (t (c_6 t+c_5)+c_4)+c_3 \]