10.4.3 problem 4

Internal problem ID [1184]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 4
Date solved : Monday, January 27, 2025 at 04:43:18 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

dsolve(diff(y(t),t) = -1+exp(y(t)),y(t), singsol=all)
 

\[ y = \ln \left (-\frac {1}{{\mathrm e}^{t} c_1 -1}\right ) \]

✓ Solution by Mathematica

Time used: 0.698 (sec). Leaf size: 28

DSolve[D[y[t],t]== -1+Exp[y[t]],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \log \left (\frac {1}{2} \left (1-\tanh \left (\frac {t+c_1}{2}\right )\right )\right ) \\ y(t)\to 0 \\ \end{align*}