23.1.129 problem 133

Internal problem ID [4736]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 133
Date solved : Tuesday, September 30, 2025 at 08:20:42 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (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: 0.572 (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: 0.098 (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)
 

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