Internal problem ID [1895]
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: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{\mathrm e}^{y} \left (y^{\prime }+1\right )=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.359 (sec). Leaf size: 32
dsolve([exp(y(x))*(diff(y(x),x)+1)=1,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -x +\ln \left (-{\mathrm e}^{x}-{\mathrm e}+1\right )-i \pi \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 18
DSolve[{Exp[y[x]]*(y'[x]+1)==1,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log \left (e^{-x} \left (e^x-1+e\right )\right ) \]