38.4.19 problem 6 (a)

Internal problem ID [8318]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 6 (a)
Date solved : Tuesday, September 30, 2025 at 05:26:18 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 13

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

\[ y = -x -1+{\mathrm e}^{2+x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to e^x \left (\int _{-2}^xe^{-K[1]} K[1]dK[1]+2 e^2\right ) \end{align*}

✓ Sympy. Time used: 0.069 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - y(x) + Derivative(y(x), x),0) 
ics = {y(-2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - x + e^{2} e^{x} - 1 \]