Internal problem ID [6725]
Book: Second order enumerated odes
Section: section 2
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 28
dsolve((2*x*y(x)^2-y(x))+(y(x)^2+x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (x^{2} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{2 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-x \right )} \]
✓ Solution by Mathematica
Time used: 0.307 (sec). Leaf size: 22
DSolve[(2*x*y[x]^2-y[x])+(y[x]^2+x+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2-\frac {x}{y(x)}+y(x)+\log (y(x))=c_1,y(x)\right ] \]