Internal problem ID [534]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+1-{\mathrm e}^{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(diff(y(t),t) = -1+exp(y(t)),y(t), singsol=all)
\[ y \relax (t ) = \ln \left (-\frac {1}{c_{1} {\mathrm e}^{t}-1}\right ) \]
✓ Solution by Mathematica
Time used: 0.817 (sec). Leaf size: 21
DSolve[y'[t]== -1+Exp[y[t]],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \log \left (\frac {1}{1+e^{t+c_1}}\right ) \\ y(t)\to 0 \\ \end{align*}