74.1.13 problem 20

Internal problem ID [15793]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 08:07:25 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y = \left (c_{2} {\mathrm e}^{7 t}+c_{1} \right ) {\mathrm e}^{-3 t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

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

\[ y(t)\to e^{-3 t} \left (c_2 e^{7 t}+c_1\right ) \]