7.5.36 problem 36

Internal problem ID [140]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 36
Date solved : Saturday, March 29, 2025 at 04:35:36 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

ode:=1+y(x)*exp(x*y(x))+(2*y(x)+x*exp(x*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: 0.263 (sec). Leaf size: 18

ode=(1+y[x]*Exp[x*y[x]])+(2*y[x]+x*Exp[x*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