44.4.20 problem 6 (b)

Internal problem ID [7033]
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 (b)
Date solved : Wednesday, March 05, 2025 at 04:03:09 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=-3 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

ode:=diff(y(x),x) = x+y(x); 
ic:=y(1) = -3; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 18

ode=D[y[x],x]==x+y[x]; 
ic={y[1]==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.149 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - y(x) + Derivative(y(x), x),0) 
ics = {y(1): -3} 
dsolve(ode,func=y(x),ics=ics)
 

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