7.1.10 problem 10

Internal problem ID [10]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.2. Problems at page 17
Problem number : 10
Date solved : Saturday, March 29, 2025 at 04:25:36 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 16

ode:=diff(y(x),x) = x*exp(-x); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 2+\left (-x -1\right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 21

ode=D[y[x],x]==x*Exp[-x]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x} \left (-x+2 e^x-1\right ) \]

✓ Sympy. Time used: 0.155 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - x e^{- x} + 2 - e^{- x} \]