78.1.33 problem 3 (a)

Internal problem ID [18017]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 3 (a)
Date solved : Monday, March 31, 2025 at 04:56:47 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 12

ode:=diff(y(x),x) = x*exp(x); 
ic:=y(1) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \left (x -1\right ) {\mathrm e}^{x}+3 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 14

ode=D[y[x],x]==x*Exp[x]; 
ic={y[1]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x (x-1)+3 \]

✓ Sympy. Time used: 0.123 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(x) + Derivative(y(x), x),0) 
ics = {y(1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x e^{x} - e^{x} + 3 \]