81.2.2 problem 3-2

Internal problem ID [21491]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 3. Exact differential equations. Page 42.
Problem number : 3-2
Date solved : Thursday, October 02, 2025 at 07:41:54 PM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.162 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.515 (sec). Leaf size: 14

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

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