15.6.9 problem 9

Internal problem ID [2966]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 9
Date solved : Sunday, March 30, 2025 at 01:02:26 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.171 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.531 (sec). Leaf size: 10

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

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