15.1.25 problem 25

Internal problem ID [2865]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 25
Date solved : Sunday, March 30, 2025 at 12:35:07 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 12

ode:=diff(y(x),x) = exp(y(x)); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\ln \left (1-x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 13

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

\[ y(x)\to -\log (1-x) \]

✓ Sympy. Time used: 0.177 (sec). Leaf size: 10

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

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