74.13.5 problem 22

Internal problem ID [16371]
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 : 22
Date solved : Tuesday, January 28, 2025 at 09:07:17 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: 0.006 (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)
 

\[ y = {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.003 (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]
 

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