43.2.1 problem 1(a)

Internal problem ID [8877]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.6 Introduction– Linear equations of First Order. Page 41
Problem number : 1(a)
Date solved : Tuesday, September 30, 2025 at 05:58:14 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-2 y&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(x),x)-2*y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {1}{2}+{\mathrm e}^{2 x} c_1 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 24

ode=D[y[x],x]-2*y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2}+c_1 e^{2 x}\\ y(x)&\to -\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.067 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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