74.13.17 problem 34

Internal problem ID [16383]
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 : 34
Date solved : Tuesday, January 28, 2025 at 09:07:22 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(t),t$5)+4*diff(y(t),t$3)=0,y(t), singsol=all)
 

\[ y = c_{1} +c_{2} t +t^{2} c_{3} +c_4 \sin \left (2 t \right )+c_5 \cos \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 60.037 (sec). Leaf size: 57

DSolve[D[ y[t],{t,5}]+4*D[ y[t],{t,3}]==0,y[t],t,IncludeSingularSolutions -> True]
 

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