32.6.50 problem Exercise 12.50, page 103

Internal problem ID [5915]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.50, page 103
Date solved : Sunday, March 30, 2025 at 10:27:11 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 20

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

\[ y = -{\mathrm e}^{x}+\ln \left (-1+{\mathrm e}^{{\mathrm e}^{x}+c_1}\right )-c_1 \]

✓ Mathematica. Time used: 2.226 (sec). Leaf size: 23

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

\begin{align*} y(x)\to \log \left (1+e^{-e^x+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.240 (sec). Leaf size: 12

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

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