73.7.39 problem 39

Internal problem ID [15126]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 39
Date solved : Monday, March 31, 2025 at 01:26:23 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x +y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 23

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

\[ y = \frac {-\ln \left (2\right )+\ln \left (-x^{2}-2 c_1 \right )}{x} \]

✓ Mathematica. Time used: 0.463 (sec). Leaf size: 20

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

\[ y(x)\to \frac {\log \left (-\frac {x^2}{2}+c_1\right )}{x} \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) + exp(-x*y(x)) + y(x)/x cannot be solved by the factorable group method