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 : Monday, January 27, 2025 at 07:04:45 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

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

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

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