65.3.4 problem 2 (D)

Internal problem ID [15641]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 2 (D)
Date solved : Thursday, October 02, 2025 at 10:21:35 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

ode=D[y[x],x]==1+y[x]; 
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: 0.060 (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)
 

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