68.5.21 problem 21

Internal problem ID [17272]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 21
Date solved : Thursday, October 02, 2025 at 02:00:34 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (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: 0.021 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to e^x \left (\int _1^xe^{-K[1]} K[1]dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.063 (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)
 

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