Internal problem ID [15160]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 298.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve((x-2*x*y(x)-y(x)^2)*diff(y(x),x)+y(x)^2=0,y(x), singsol=all)
\[ y = \frac {1}{\operatorname {RootOf}\left (-\textit {\_Z}^{2} x +{\mathrm e}^{\textit {\_Z}} c_{1} +1\right )} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 23
DSolve[(x-2*x*y[x]-y[x]^2)*y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=y(x)^2+c_1 e^{\frac {1}{y(x)}} y(x)^2,y(x)\right ] \]