50.17.4 problem 1(b) solving directly

Internal problem ID [8075]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of First-Order Differential Equations Page 162
Problem number : 1(b) solving directly
Date solved : Wednesday, March 05, 2025 at 05:29:17 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

ode:=diff(y(x),x)+y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.112 (sec). Leaf size: 8

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

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