89.6.1 problem 1

Internal problem ID [24384]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:22:49 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.581 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.135 (sec). Leaf size: 12

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)
 

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