76.24.10 problem 12

Internal problem ID [17809]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 11:03:17 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(t),t$4)+diff(y(t),t$2)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 24

DSolve[D[y[t],{t,4}]+D[y[t],{t,2}]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_4 t-c_1 \cos (t)-c_2 \sin (t)+c_3 \]