57.1.53 problem 53

Internal problem ID [9037]
Book : First order enumerated odes
Section : section 1
Problem number : 53
Date solved : Monday, January 27, 2025 at 05:27:47 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} {y^{\prime }}^{2}&=\frac {y^{3}}{x} \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 27

dsolve(diff(y(x),x)^2=y(x)^3/x,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \frac {\operatorname {WeierstrassP}\left (1, 0, 0\right ) 2^{{2}/{3}}}{\left (\sqrt {x}\, 2^{{1}/{3}}+c_{1} \right )^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 42

DSolve[(D[y[x],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*}