8.6.17 problem 17

Internal problem ID [787]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 17
Date solved : Saturday, March 29, 2025 at 10:25:09 PM
CAS classification : [_exact]

\begin{align*} {\mathrm e}^{x}+{\mathrm e}^{x y} y+\left ({\mathrm e}^{y}+{\mathrm e}^{x y} x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 15

ode:=exp(x)+exp(x*y(x))*y(x)+(exp(y(x))+exp(x*y(x))*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ {\mathrm e}^{x y}+{\mathrm e}^{x}+{\mathrm e}^{y}+c_1 = 0 \]

✓ Mathematica. Time used: 0.211 (sec). Leaf size: 20

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

\[ \text {Solve}\left [e^{y(x)}+e^{x y(x)}+e^x=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out