14.1.22 problem Problem 30

Internal problem ID [3579]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 30
Date solved : Tuesday, September 30, 2025 at 06:46:05 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.122 (sec). Leaf size: 10

ode:=diff(y(x),x) = (1-y(x)*exp(x*y(x)))/x/exp(x*y(x)); 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\ln \left (x \right )}{x} \]

✓ Mathematica. Time used: 0.252 (sec). Leaf size: 11

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

\begin{align*} y(x)&\to \frac {\log (x)}{x} \end{align*}

✗ Sympy

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

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