Internal problem ID [7757]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 177.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 18
dsolve(x^2*(x-1)*diff(y(x),x) - y(x)^2 - x*(x-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{c_{1} x -c_{1}+1} \]
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 25
DSolve[x^2*(x-1)*y'[x] - y[x]^2 - x*(x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{c_1 (-x)+1+c_1} \\ y(x)\to 0 \\ \end{align*}