Internal problem ID [8433]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 853.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {14 y x +12+2 x +y^{3} x^{3}+6 y^{2} x^{2}}{x^{2} \left (y x +2+x \right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve(diff(y(x),x) = 1/x^2*(14*x*y(x)+12+2*x+x^3*y(x)^3+6*x^2*y(x)^2)/(x*y(x)+2+x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2 \sqrt {c_{1}-2 x}-x -2}{x \left (\sqrt {c_{1}-2 x}-1\right )} \\ y \relax (x ) = -\frac {2 \sqrt {c_{1}-2 x}+x +2}{x \left (\sqrt {c_{1}-2 x}+1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.381 (sec). Leaf size: 84
DSolve[y'[x] == (12 + 2*x + 14*x*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^3)/(x^2*(2 + x + x*y[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-2 \sqrt {-2 x+c_1}+2}{x \left (-1+\sqrt {-2 x+c_1}\right )} \\ y(x)\to -\frac {x+2 \sqrt {-2 x+c_1}+2}{x+x \sqrt {-2 x+c_1}} \\ y(x)\to -\frac {2}{x} \\ \end{align*}