83.8.23 problem 24

Internal problem ID [19070]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 24
Date solved : Friday, March 14, 2025 at 05:04:34 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 5.485 (sec). Leaf size: 29

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

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

✓ Sympy. Time used: 0.889 (sec). Leaf size: 15

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

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