Internal problem ID [3874]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 3
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _dAlembert]
Solve \begin {gather*} \boxed {1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 20
dsolve((1+exp(x/y(x)))+exp(x/y(x))*(1-x/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{\LambertW \left (\frac {x c_{1}}{c_{1} x -1}\right )} \]
✓ Solution by Mathematica
Time used: 1.315 (sec). Leaf size: 34
DSolve[(1+Exp[x/y[x]])+Exp[x/y[x]]*(1-x/y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\text {ProductLog}\left (\frac {x}{x-e^{c_1}}\right )} \\ y(x)\to -e^{\text {ProductLog}(1)} x \\ \end{align*}