Internal problem ID [8262]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 682.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 a}{x \left (-y x +2 a x y^{2}-8 a^{2}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x) = 2*a/x/(-x*y(x)+2*a*x*y(x)^2-8*a^2),y(x), singsol=all)
\[ c_{1}+\frac {\left (-y \relax (x )^{2} x +4 a \right ) {\mathrm e}^{-4 a y \relax (x )}}{x} = 0 \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 39
DSolve[y'[x] == (2*a)/(x*(-8*a^2 - x*y[x] + 2*a*x*y[x]^2)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^2 e^{-4 a y(x)}}{8 a}-\frac {e^{-4 a y(x)}}{2 x}=c_1,y(x)\right ] \]