Internal problem ID [3081]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 333.
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 (1-2 x \right ) y^{\prime }-4 x +\left (4 x +1\right ) y-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(x*(1-2*x)*diff(y(x),x) = 4*x-(1+4*x)*y(x)+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {-2 x^{2}+c_{1}}{-x +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 27
DSolve[x(1-2 x)y'[x]==4 x -(1+4 x)y[x]+y[x]^2,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*}