44.2.20 problem 20

Internal problem ID [6952]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 20
Date solved : Wednesday, March 05, 2025 at 02:54:27 AM
CAS classification : [[_linear, `class A`]]

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

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

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

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 16

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

\[ y(x)\to -x+c_1 e^x-1 \]

✓ Sympy. Time used: 0.140 (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)
 

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