75.4.7 problem 52

Internal problem ID [16638]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 52
Date solved : Monday, March 31, 2025 at 03:02:47 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 16

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

\[ y(x)\to -\log (-x-c_1) \]

✓ Sympy. Time used: 0.161 (sec). Leaf size: 10

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

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