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 : Sunday, March 30, 2025 at 11:15:33 AM
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*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 29

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

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

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

ode=(y[x]+Exp[y[x]]-Exp[-x])+(1+Exp[y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 2.056 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((exp(y(x)) + 1)*Derivative(y(x), x) + y(x) + exp(y(x)) - exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (- C_{1} + x - e^{x} W\left (e^{- \left (C_{1} - x\right ) e^{- x}}\right )\right ) e^{- x} \]