74.1.32 problem 39

Internal problem ID [15812]
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 : Tuesday, January 28, 2025 at 08:08:02 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 24

DSolve[D[y[x],x]==x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

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