7.7.1 problem 1

Internal problem ID [2364]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2, linear equations with constant coefficients. Page 138
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 05:34:54 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.026 (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)
 

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