Internal problem ID [8403]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 823.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (x +y\right )}{x \left (x +y+y^{3}+y^{4}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (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)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-2 \,{\mathrm e}^{4 \textit {\_Z}}-3 \,{\mathrm e}^{3 \textit {\_Z}}+6 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (x )+6 c_{1} {\mathrm e}^{\textit {\_Z}}-6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+6 x \right )} \]
✓ Solution by Mathematica
Time used: 0.283 (sec). Leaf size: 39
DSolve[y'[x] == (y[x]*(x + y[x]))/(x*(x + y[x] + y[x]^3 + y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^3}{3}+\frac {y(x)^2}{2}+\log (y(x))-\frac {y(x) \log (x)+x}{y(x)}=c_1,y(x)\right ] \]