14.21.2 problem 2

Internal problem ID [2711]
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 : 2
Date solved : Monday, January 27, 2025 at 06:12:11 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(t),t$3)-6*diff(y(t),t$2)+5*diff(y(t),t)+12*y(t)=0,y(t), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{4 t}+c_2 \,{\mathrm e}^{-t}+c_3 \,{\mathrm e}^{3 t} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

DSolve[D[y[t],{t,3}]-6*D[y[t],{t,2}]+5*D[y[t],t]+12*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (e^{4 t} \left (c_3 e^t+c_2\right )+c_1\right ) \]