14.21.1 problem 1

Internal problem ID [2710]
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 : 1
Date solved : Monday, January 27, 2025 at 06:12:11 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

\[ y = {\mathrm e}^{2 t} c_1 +c_2 \,{\mathrm e}^{t}+c_3 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 28

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

\[ y(t)\to c_1 e^{-t}+c_2 e^t+c_3 e^{2 t} \]