Internal problem ID [2055]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _dAlembert]
\[ \boxed {{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (x \right ) = -\frac {x}{\operatorname {LambertW}\left (\frac {x c_{1}}{c_{1} x -1}\right )} \]
✓ Solution by Mathematica
Time used: 1.251 (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}{W\left (\frac {x}{x-e^{c_1}}\right )} \\ y(x)\to -\frac {x}{W(1)} \\ \end{align*}