43.1.6 problem 2 (c)

Internal problem ID [8871]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number : 2 (c)
Date solved : Tuesday, September 30, 2025 at 05:58:08 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.024 (sec). Leaf size: 12

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

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