51.1.53 problem 53

Internal problem ID [10323]
Book : First order enumerated odes
Section : section 1
Problem number : 53
Date solved : Tuesday, September 30, 2025 at 07:19:25 PM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 27

ode:=diff(y(x),x)^2 = y(x)^3/x; 
dsolve(ode,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*}

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 42

ode=(D[y[x],x])^2==y[x]^3/x; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 7.563 (sec). Leaf size: 80

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**2 - y(x)**3/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}^{6} - 2 C_{1}^{5} \sqrt {x} - C_{1}^{4} x + 4 C_{1}^{3} x^{\frac {3}{2}} - C_{1}^{2} x^{2} - 2 C_{1} x^{\frac {5}{2}} + x^{3}}{C_{1}^{8} - 4 C_{1}^{6} x + 6 C_{1}^{4} x^{2} - 4 C_{1}^{2} x^{3} + x^{4}} \]