Internal problem ID [14212]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 54.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-{\mathrm e}^{-y+x}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 11
dsolve([diff(y(x),x)=exp(x-y(x)),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left ({\mathrm e}^{x}-1+{\mathrm e}\right ) \]
✓ Solution by Mathematica
Time used: 0.687 (sec). Leaf size: 12
DSolve[{y'[x]==Exp[x-y[x]],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log \left (e^x-1+e\right ) \]