Internal problem ID [1895]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {{\mathrm e}^{y} \left (y^{\prime }+1\right )-1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.279 (sec). Leaf size: 32
dsolve([exp(y(x))*(diff(y(x),x)+1)=1,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -x +\ln \left (-{\mathrm e}^{x}-{\mathrm e}+1\right )-i \pi \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 17
DSolve[{Exp[y[x]]*(y'[x]+1)==1,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left ((e-1) e^{-x}+1\right ) \\ \end{align*}