8.5.36 problem 36

Internal problem ID [764]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 36
Date solved : Saturday, March 29, 2025 at 10:20:28 PM
CAS classification : [_exact]

\begin{align*} 1+{\mathrm e}^{x y} y+\left ({\mathrm e}^{x y} x +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

ode:=1+exp(x*y(x))*y(x)+(exp(x*y(x))*x+2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x +{\mathrm e}^{x y}+y^{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.244 (sec). Leaf size: 18

ode=1+Exp[x*y[x]]*y[x]+(Exp[x*y[x]]*x+2*y[x])*D[y[x],x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [y(x)^2+e^{x y(x)}+x=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x*exp(x*y(x)) + 2*y(x))*Derivative(y(x), x) + y(x)*exp(x*y(x)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out