73.6.10 problem 7.4 (h)

Internal problem ID [15149]
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)
Date solved : Tuesday, January 28, 2025 at 07:38:07 AM
CAS classification : [[_1st_order, _with_exponential_symmetries], _exact]

\begin{align*} {\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 13

dsolve(exp(y(x))+(x*exp(y(x))+1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\operatorname {LambertW}\left (x \,{\mathrm e}^{c_{1}}\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 4.451 (sec). Leaf size: 17

DSolve[Exp[y[x]]+(x*Exp[y[x]]+1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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