Internal problem ID [8311]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 731.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 y+1}{x \left (2 x y^{3}+x y^{2}-2\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve(diff(y(x),x) = 1/x*(1+2*y(x))/(-2+x*y(x)^2+2*x*y(x)^3),y(x), singsol=all)
\begin{align*} y \relax (x ) = -{\frac {1}{2}} \\ y \relax (x ) = \frac {{\mathrm e}^{\RootOf \left (x \,{\mathrm e}^{3 \textit {\_Z}}-4 x \,{\mathrm e}^{2 \textit {\_Z}}+8 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+3 x \,{\mathrm e}^{\textit {\_Z}}+16\right )}}{2}-\frac {1}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.341 (sec). Leaf size: 47
DSolve[y'[x] == (1 + 2*y[x])/(x*(-2 + x*y[x]^2 + 2*x*y[x]^3)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{64} \left (-4 y(x)^2+4 y(x)-2 \log (8 y(x)+4)+3\right )-\frac {1}{4 x (2 y(x)+1)}=c_1,y(x)\right ] \]