74.9.1 problem 9

Internal problem ID [16098]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 9
Date solved : Thursday, March 13, 2025 at 07:51:38 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.049 (sec). Leaf size: 12

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

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