21.4 problem 1(d)

Internal problem ID [5313]

Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {{\mathrm e}^{x -y}}{1+{\mathrm e}^{x}}=0} \end {gather*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

\[ y \relax (x ) = \ln \left (\ln \left ({\mathrm e}^{x}+1\right )+c_{1}\right ) \]

Solution by Mathematica

Time used: 0.457 (sec). Leaf size: 15

DSolve[y'[x]==Exp[x-y[x]]/(1+Exp[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \log \left (\log \left (e^x+1\right )+c_1\right ) \\ \end{align*}