71.6.2 problem 2

Internal problem ID [14337]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 2
Date solved : Monday, March 31, 2025 at 12:18:14 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 5

ode:=diff(y(x),x) = 1-y(x); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 1 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

ode=D[y[x],x]==-y[x]+1; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 1 \]

✓ Sympy. Time used: 0.106 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = 1 \]