Internal problem ID [8408]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 830.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {y^{\prime }-\frac {y \left (x -y\right )}{x \left (x -y-y^{3}-y^{4}\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x) = y(x)*(x-y(x))/x/(x-y(x)-y(x)^3-y(x)^4),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (2 \,{\mathrm e}^{4 \textit {\_Z}}+3 \,{\mathrm e}^{3 \textit {\_Z}}-6 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+6 c_{1} {\mathrm e}^{\textit {\_Z}}+6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+6 x \right )} \]
✓ Solution by Mathematica
Time used: 0.299 (sec). Leaf size: 37
DSolve[y'[x] == ((x - y[x])*y[x])/(x*(x - y[x] - y[x]^3 - y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{3} y(x)^3-\frac {y(x)^2}{2}-\frac {x}{y(x)}-\log (y(x))+\log (x)=c_1,y(x)\right ] \]