Internal problem ID [15023]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 116.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {2 x y^{\prime } \left (-y^{2}+x \right )+y^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(2*x*diff(y(x),x)*(x-y(x)^2)+y(x)^3=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {c_{1}}{2}}}{\sqrt {-\frac {{\mathrm e}^{c_{1}}}{x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{c_{1}}}{x}\right )}}} \]
✓ Solution by Mathematica
Time used: 6.48 (sec). Leaf size: 60
DSolve[2*x*y'[x]*(x-y[x]^2)+y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i \sqrt {x} \sqrt {W\left (-\frac {e^{c_1}}{x}\right )} \\ y(x)\to i \sqrt {x} \sqrt {W\left (-\frac {e^{c_1}}{x}\right )} \\ y(x)\to 0 \\ \end{align*}