72.1.6 problem 9

Internal problem ID [14606]
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 : Tuesday, January 28, 2025 at 06:44:18 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 8

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

\[ y = \ln \left (t +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 10

DSolve[D[y[t],t]==Exp[-y[t]],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \log (t+c_1) \]