Internal problem ID [9314]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 980.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]
\[ \boxed {y^{\prime }-\frac {x^{3} y^{3}+6 x^{2} y^{2}+12 x y+8+2 x}{x^{3}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x) = (x^3*y(x)^3+6*x^2*y(x)^2+12*x*y(x)+8+2*x)/x^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {1}{\sqrt {-2 x +c_{1}}}-\frac {2}{x} \\ y \left (x \right ) &= \frac {1}{\sqrt {-2 x +c_{1}}}-\frac {2}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 53
DSolve[y'[x] == (8 + 2*x + 12*x*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^3)/x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2+\frac {x}{\sqrt {-2 x+c_1}}}{x} \\ y(x)\to -\frac {2}{x}+\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {2}{x} \\ \end{align*}