Internal problem ID [7736]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 156.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }-y \left (y-x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve((x^2-1)*diff(y(x),x) - y(x)*(y(x)-x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1}+x} \]
✓ Solution by Mathematica
Time used: 0.281 (sec). Leaf size: 26
DSolve[(x^2-1)*y'[x] - y[x]*(y[x]-x)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x+c_1 \sqrt {x^2-1}} \\ y(x)\to 0 \\ \end{align*}