Internal problem ID [6616]
Book: First order enumerated odes
Section: section 1
Problem number: 53.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\frac {y^{3}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.329 (sec). Leaf size: 29
dsolve(diff(y(x),x)^2=y(x)^3/x,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \WeierstrassP \left (\frac {x 2^{\frac {2}{3}}}{\sqrt {2^{\frac {2}{3}} x}}+c_{1}, 0, 0\right ) 2^{\frac {2}{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.12 (sec). Leaf size: 42
DSolve[(y'[x])^2==y[x]^3/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4}{\left (-2 \sqrt {x}+c_1\right ){}^2} \\ y(x)\to \frac {4}{\left (2 \sqrt {x}+c_1\right ){}^2} \\ y(x)\to 0 \\ \end{align*}