36.3.4 problem 4

Internal problem ID [6325]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 4
Date solved : Wednesday, March 05, 2025 at 12:35:09 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 19

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

\[ {\mathrm e}^{y \left (x \right ) x}+x^{2}-y \left (x \right )^{2}+c_{1} = 0 \]

✓ Mathematica. Time used: 0.292 (sec). Leaf size: 22

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

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

✗ Sympy

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

Timed Out