Internal problem ID [15124]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 11. Singular solutions of differential equations. Exercises page 92
Problem number: 262.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 29
dsolve(diff(y(x),x)^3-4*x*y(x)*diff(y(x),x)+8*y(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {4 x^{3}}{27} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (4 c_{1} x -1\right )^{2}}{64 c_{1}^{3}} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]^3-4*x*y[x]*y'[x]+8*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Timed out