Internal problem ID [8357]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 777.
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 {y \left (1+y\right )}{x \left (-y-1+x y^{4}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 59
dsolve(diff(y(x),x) = y(x)*(y(x)+1)/x/(-y(x)-1+x*y(x)^4),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -1 \\ y \relax (x ) = {\mathrm e}^{\RootOf \left (x \,{\mathrm e}^{3 \textit {\_Z}}-5 x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} x +7 \,{\mathrm e}^{\textit {\_Z}} x -2 c_{1} x -2 \textit {\_Z} x -3 x +2\right )}-1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.213 (sec). Leaf size: 39
DSolve[y'[x] == (y[x]*(1 + y[x]))/(x*(-1 - y[x] + x*y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{2} (y(x)+1)^2+2 (y(x)+1)-\frac {1}{x y(x)}-\log (y(x)+1)=c_1,y(x)\right ] \]