Internal problem ID [9074]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 739.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y^{\prime }-\frac {1+2 y}{x \left (-2+y x +2 y^{2} x \right )}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(x),x) = 1/x*(1+2*y(x))/(-2+x*y(x)+2*x*y(x)^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -{\frac {1}{2}} \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x \,{\mathrm e}^{\textit {\_Z}}-\textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}+4\right )}}{2}-\frac {1}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.244 (sec). Leaf size: 39
DSolve[y'[x] == (1 + 2*y[x])/(x*(-2 + x*y[x] + 2*x*y[x]^2)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{8} (-2 y(x)+\log (4 y(x)+2)-1)-\frac {1}{2 x (2 y(x)+1)}=c_1,y(x)\right ] \]