12.1.9 problem 4(a)

Internal problem ID [1527]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 4(a)
Date solved : Tuesday, March 04, 2025 at 12:38:08 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: 0.006 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.120 (sec). Leaf size: 10

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)
 

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