Internal problem ID [9188]
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`]]
\[ \boxed {y^{\prime }-\frac {14 y x +12+2 x +y^{3} x^{3}+6 y^{2} x^{2}}{x^{2} \left (y x +2+x \right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
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 \left (x \right ) &= \frac {-2 \sqrt {-2 x +c_{1}}+x +2}{\left (\sqrt {-2 x +c_{1}}-1\right ) x} \\ y \left (x \right ) &= \frac {-2 \sqrt {-2 x +c_{1}}-x -2}{\left (\sqrt {-2 x +c_{1}}+1\right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.399 (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*}