11.1.4 problem 9

Internal problem ID [1465]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number : 9
Date solved : Monday, January 27, 2025 at 04:57:42 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: 0.004 (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)
 

\[ y = \left (c_2 \,{\mathrm e}^{3 t}+c_3 \,{\mathrm e}^{t}+c_1 \right ) {\mathrm e}^{-2 t} \]

✓ 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]
 

\[ y(t)\to e^{-2 t} \left (c_2 e^t+c_3 e^{3 t}+c_1\right ) \]