Internal problem ID [8398]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 818.
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}{x \left (-1+x y+x y^{3}+x y^{4}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 34
dsolve(diff(y(x),x) = y(x)/x/(-1+x*y(x)+x*y(x)^3+x*y(x)^4),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-2 \,{\mathrm e}^{4 \textit {\_Z}} x -3 x \,{\mathrm e}^{3 \textit {\_Z}}+6 c_{1} x \,{\mathrm e}^{\textit {\_Z}}-6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} x -6\right )} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 34
DSolve[y'[x] == y[x]/(x*(-1 + x*y[x] + x*y[x]^3 + x*y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^3}{3}+\frac {y(x)^2}{2}+\frac {1}{x y(x)}+\log (y(x))=c_1,y(x)\right ] \]