68.1.32 problem 39

Internal problem ID [17099]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 39
Date solved : Thursday, October 02, 2025 at 01:43:12 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \left (-x -1\right ) {\mathrm e}^{-x}+c_1 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.072 (sec). Leaf size: 14

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

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