Internal problem ID [10162]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary.
Page 29
Problem number: Ex 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1-x \right ) y+\left (1-y\right ) x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve((1-x)*y(x)+(1-y(x))*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\LambertW \left (-\frac {{\mathrm e}^{x} c_{1}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 60.03 (sec). Leaf size: 21
DSolve[(1-x)*y[x]+(1-y[x])*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ProductLog}\left (-\frac {e^{x-c_1}}{x}\right ) \\ \end{align*}