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 : Monday, January 27, 2025 at 06:20:45 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*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 12

dsolve([diff(y(x),x)=exp(y(x)),y(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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