Internal problem ID [3789]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 537.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y \left (1-x \right ) y^{\prime }+x \left (1-y\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(y(x)*(1-x)*diff(y(x),x)+x*(1-y(x)) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {LambertW}\left (\frac {{\mathrm e}^{-x -1}}{c_{1} \left (x -1\right )}\right )+1 \]
✓ Solution by Mathematica
Time used: 8.099 (sec). Leaf size: 28
DSolve[y[x](1-x)y'[x]+x(1-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+W\left (\frac {e^{-x-1+c_1}}{x-1}\right ) y(x)\to 1 \end{align*}