66.1.8 problem Problem 8

Internal problem ID [13784]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 8
Date solved : Monday, March 31, 2025 at 08:11:46 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.757 (sec). Leaf size: 12

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

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

✓ Sympy. Time used: 0.167 (sec). Leaf size: 8

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

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