Internal problem ID [10201]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
26. Equations solvable for \(x\). Page 55
Problem number: Ex 4.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-4 y x y^{\prime }+8 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 36
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 \relax (x ) = \frac {4 x^{3}}{27} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {x^{2}}{4 c_{1}}-\frac {x}{8 c_{1}^{2}}+\frac {1}{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