Internal problem ID [4061]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.48, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (2 x y^{3}+x y+x^{2}\right ) y^{\prime }-x y+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 29
dsolve((2*x*y(x)^3+x*y(x)+x^2)*diff(y(x),x)-x*y(x)+y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-{\mathrm e}^{3 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \relax (x )+c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )} \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 23
DSolve[(2*x*y[x]^3+x*y[x]+x^2)*y'[x]-x*y[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)^2-\frac {x}{y(x)}+\log (y(x))+\log (x)=c_1,y(x)\right ] \]