Internal problem ID [8653]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 317.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {\left (2 y^{3} x +y x +x^{2}\right ) y^{\prime }+y^{2}-y x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve((2*x*y(x)^3+x*y(x)+x^2)*diff(y(x),x)+y(x)^2-x*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )} \]
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 23
DSolve[-(x*y[x]) + y[x]^2 + (x^2 + x*y[x] + 2*x*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)^2-\frac {x}{y(x)}+\log (y(x))+\log (x)=c_1,y(x)\right ] \]