Internal problem ID [8506]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 926.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-8 x^{2} y^{3}+16 x y^{2}+16 x y^{3}-8+12 y x -6 y^{2} x^{2}+y^{3} x^{3}}{16 \left (-2+y x -2 y\right ) x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve(diff(y(x),x) = 1/16*(-8*x^2*y(x)^3+16*x*y(x)^2+16*x*y(x)^3-8+12*x*y(x)-6*x^2*y(x)^2+x^3*y(x)^3)/(-2+x*y(x)-2*y(x))/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {2 \sqrt {c_{1}+8 \ln \relax (x )}+8}{x \sqrt {c_{1}+8 \ln \relax (x )}+4 x -8} \\ y \relax (x ) = \frac {2 \sqrt {c_{1}+8 \ln \relax (x )}-8}{x \sqrt {c_{1}+8 \ln \relax (x )}-4 x +8} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.526 (sec). Leaf size: 86
DSolve[y'[x] == (-1/2 + (3*x*y[x])/4 + x*y[x]^2 - (3*x^2*y[x]^2)/8 + x*y[x]^3 - (x^2*y[x]^3)/2 + (x^3*y[x]^3)/16)/(x*(-2 - 2*y[x] + x*y[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 \left (-64+\sqrt {2048 \log (x)+c_1}\right )}{128+x \left (-64+\sqrt {2048 \log (x)+c_1}\right )} \\ y(x)\to \frac {2 \left (64+\sqrt {2048 \log (x)+c_1}\right )}{-128+x \left (64+\sqrt {2048 \log (x)+c_1}\right )} \\ y(x)\to \frac {2}{x} \\ \end{align*}