84.11.4 problem 6.4

Internal problem ID [22141]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 6. Exact first-order differential equations. Solved problems. Page 24
Problem number : 6.4
Date solved : Thursday, October 02, 2025 at 08:31:41 PM
CAS classification : [`x=_G(y,y')`]

\begin{align*} y^{\prime }&=\frac {2+y \,{\mathrm e}^{y x}}{2 y-x \,{\mathrm e}^{y x}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.168 (sec). Leaf size: 22

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

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

✗ Sympy

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

Timed Out