71.6.3 problem 3

Internal problem ID [14338]
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 : 3
Date solved : Monday, March 31, 2025 at 12:18:15 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 10

ode:=diff(y(x),x) = 1-y(x); 
ic:=y(0) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 12

ode=D[y[x],x]==-y[x]+1; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x}+1 \]

✓ 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 = {y(0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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