Internal problem ID [7735]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 155.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 14
dsolve((x^2-1)*diff(y(x),x) + y(x)^2 - 2*x*y(x) + 1=0,y(x), singsol=all)
\[ y \relax (x ) = x +\frac {1}{-\arctanh \relax (x )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.261 (sec). Leaf size: 21
DSolve[(x^2-1)*y'[x]+ y[x]^2 - 2*x*y[x] + 1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {1}{-\tanh ^{-1}(x)+c_1} \\ y(x)\to x \\ \end{align*}