Internal problem ID [7745]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 165.
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 {x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (4 x +1\right ) y+4 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 17
dsolve(x*(2*x-1)*diff(y(x),x) + y(x)^2 - (4*x+1)*y(x) + 4*x=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x^{2}+c_{1}}{c_{1}+x} \]
✓ Solution by Mathematica
Time used: 0.226 (sec). Leaf size: 27
DSolve[x*(2*x-1)*y'[x] + y[x]^2 - (4*x+1)*y[x] + 4*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\frac {x (2 x-1)}{x-c_1} \\ y(x)\to 1 \\ \end{align*}