Internal problem ID [8453]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 873.
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 {1+2 y}{x \left (-2+x +x y^{2}+3 x y^{3}+2 x y+2 x y^{4}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 54
dsolve(diff(y(x),x) = 1/x*(1+2*y(x))/(-2+x+x*y(x)^2+3*x*y(x)^3+2*x*y(x)+2*x*y(x)^4),y(x), singsol=all)
\begin{align*} y \relax (x ) = -{\frac {1}{2}} \\ y \relax (x ) = \frac {{\mathrm e}^{\RootOf \left (2 \,{\mathrm e}^{4 \textit {\_Z}} x -3 x \,{\mathrm e}^{3 \textit {\_Z}}-6 x \,{\mathrm e}^{2 \textit {\_Z}}+48 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} x +7 \,{\mathrm e}^{\textit {\_Z}} x +96\right )}}{2}-\frac {1}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.547 (sec). Leaf size: 53
DSolve[y'[x] == (1 + 2*y[x])/(x*(-2 + x + 2*x*y[x] + x*y[x]^2 + 3*x*y[x]^3 + 2*x*y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{192} \left (-16 y(x)^3-12 y(x)^2+12 y(x)-54 \log (4 y(x)+2)+7\right )-\frac {1}{2 x (2 y(x)+1)}=c_1,y(x)\right ] \]