Internal problem ID [7836]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 256.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (y-1\right ) y^{\prime }+\left (-1+x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 31
dsolve(x^2*(y(x)-1)*diff(y(x),x)+(x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {\ln \relax (x ) x -\LambertW \left (-x \,{\mathrm e}^{c_{1}+\frac {1}{x}}\right ) x +c_{1} x +1}{x}} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 21
DSolve[x^2*(y[x]-1)*y'[x]+(x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\operatorname {ProductLog}\left (x \left (-e^{\frac {1}{x}-c_1}\right )\right ) \\ \end{align*}