Internal problem ID [8378]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 798.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (x +y+1\right ) y}{\left (x +y+2 y^{3}\right ) \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 30
dsolve(diff(y(x),x) = 1/(2*y(x)^3+y(x)+x)*(x+y(x)+1)*y(x)/(x+1),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-{\mathrm e}^{3 \textit {\_Z}}+\ln \left (x +1\right ) {\mathrm e}^{\textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )} \]
✓ Solution by Mathematica
Time used: 0.361 (sec). Leaf size: 27
DSolve[y'[x] == (y[x]*(1 + x + y[x]))/((1 + x)*(x + y[x] + 2*y[x]^3)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)^2-\frac {x}{y(x)}+\log (y(x))-\log (x+1)=c_1,y(x)\right ] \]