Internal problem ID [1995]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries]]
\[ \boxed {-\left ({\mathrm e}^{y}+x \right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve(1=(x+exp(y(x)))*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {LambertW}\left (x \,{\mathrm e}^{c_{1}}\right )-c_{1} \]
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 17
DSolve[1==(x+Exp[y[x]])*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to W\left (e^{c_1} x\right )-c_1 \]