14.21.4 problem 4

Internal problem ID [2713]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.15, Higher order equations. Excercises page 263
Problem number : 4
Date solved : Monday, January 27, 2025 at 06:12:12 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

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

dsolve(diff(y(t),t$3)-diff(y(t),t$2)+diff(y(t),t)-y(t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{t} c_1 +\sin \left (t \right ) c_2 +\cos \left (t \right ) c_3 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

DSolve[D[y[t],{t,3}]-D[y[t],{t,2}]+D[y[t],t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_3 e^t+c_1 \cos (t)+c_2 \sin (t) \]