89.6.34 problem 35

Internal problem ID [24417]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 35
Date solved : Thursday, October 02, 2025 at 10:26:30 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.2 (sec). Leaf size: 17

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

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

✗ Sympy

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

Timed Out