Internal problem ID [7369]
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`]]
\[ \boxed {{y^{\prime }}^{2}-\frac {y^{3}}{x}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 29
dsolve(diff(y(x),x)^2=y(x)^3/x,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \operatorname {WeierstrassP}\left (\frac {x 2^{\frac {2}{3}}}{\sqrt {x 2^{\frac {2}{3}}}}+c_{1} , 0, 0\right ) 2^{\frac {2}{3}} \end{align*}
✓ Solution by Mathematica
Time used: 0.073 (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*}