2.2.2 problem 2

Internal problem ID [662]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 04:05:07 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.062 (sec). Leaf size: 10

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

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