68.1.13 problem 20

Internal problem ID [17080]
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 : Thursday, October 02, 2025 at 01:42:47 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)-diff(y(t),t)-12*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to e^{-3 t} \left (c_2 e^{7 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-12*y(t) - Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 3 t} + C_{2} e^{4 t} \]