57.1.66 problem 66

Internal problem ID [9050]
Book : First order enumerated odes
Section : section 1
Problem number : 66
Date solved : Sunday, March 30, 2025 at 02:05:33 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (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: 0.82 (sec). Leaf size: 18

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: 0.176 (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)
 

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