40.4.25 problem 23 (e)

Internal problem ID [6665]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 23 (e)
Date solved : Monday, January 27, 2025 at 02:18:34 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 29

dsolve((y(x)+exp(y(x))-exp(-x))+(1+exp(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\operatorname {LambertW}\left ({\mathrm e}^{{\mathrm e}^{-x} \left (x -c_1 \right )}\right )+{\mathrm e}^{-x} \left (x -c_1 \right ) \]

✓ Solution by Mathematica

Time used: 6.093 (sec). Leaf size: 33

DSolve[(y[x]+Exp[y[x]]-Exp[-x])+(1+Exp[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (-e^x W\left (e^{e^{-x} (x+c_1)}\right )+x+c_1\right ) \]