Internal problem ID [8592]
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]
\[ \boxed {x^{2} \left (y-1\right ) y^{\prime }+\left (x -1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(x^2*(y(x)-1)*diff(y(x),x)+(x-1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {\ln \left (x \right ) x -\operatorname {LambertW}\left (-x \,{\mathrm e}^{c_{1} +\frac {1}{x}}\right ) x +x c_{1} +1}{x}} \]
✓ Solution by Mathematica
Time used: 2.975 (sec). Leaf size: 26
DSolve[x^2*(y[x]-1)*y'[x]+(x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -W\left (x \left (-e^{\frac {1}{x}-c_1}\right )\right ) y(x)\to 0 \end{align*}