Internal problem ID [5322]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y+{\mathrm e}^{y}+\left (1+{\mathrm e}^{y}\right ) y^{\prime }={\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (x \right ) = -\operatorname {LambertW}\left ({\mathrm e}^{{\mathrm e}^{-x} \left (x -c_{1} \right )}\right )+{\mathrm e}^{-x} \left (x -c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 6.265 (sec). Leaf size: 33
DSolve[(y[x]+Exp[y[x]]-Exp[-x])+(1+Exp[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (-e^x W\left (e^{e^{-x} (x+c_1)}\right )+x+c_1\right ) \]