66.1.6 problem 9

Internal problem ID [15893]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.2. page 33
Problem number : 9
Date solved : Thursday, October 02, 2025 at 10:29:18 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 8

ode:=diff(y(t),t) = exp(-y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \ln \left (t +c_1 \right ) \]

✓ Mathematica. Time used: 0.142 (sec). Leaf size: 10

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

\begin{align*} y(t)&\to \log (t+c_1) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 7

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

\[ y{\left (t \right )} = \log {\left (C_{1} + t \right )} \]