10.2.7 problem 7

Internal problem ID [1135]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 7
Date solved : Saturday, March 29, 2025 at 10:40:58 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x*exp(x) - 1)*exp(-x)/(x + exp(y(x))) cannot be solved by the factorable group method