19.1.3 problem 3

Internal problem ID [3517]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 04:44:00 PM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{x +y} y^{\prime }-1&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 15

ode:=exp(x+y(x))*diff(y(x),x)-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 16

ode=Exp[x+y[x]]*D[y[x],x]-1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.200 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(exp(x + y(x))*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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