Internal problem ID [13413]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.4 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries], _exact]
\[ \boxed {{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(exp(y(x))+(x*exp(y(x))+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (x \,{\mathrm e}^{c_{1}}\right )+c_{1} \]
✓ Solution by Mathematica
Time used: 4.529 (sec). Leaf size: 17
DSolve[Exp[y[x]]+(x*Exp[y[x]]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1-W\left (e^{c_1} x\right ) \]