51.1.57 problem 57

Internal problem ID [10327]
Book : First order enumerated odes
Section : section 1
Problem number : 57
Date solved : Tuesday, September 30, 2025 at 07:19:31 PM
CAS classification : [_separable]

\begin{align*} {y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 29

ode:=diff(y(x),x)^2 = 1/x^2/y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \ln \left (x \right )-\frac {2 y^{{5}/{2}}}{5}-c_1 &= 0 \\ \ln \left (x \right )+\frac {2 y^{{5}/{2}}}{5}-c_1 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 45

ode=(D[y[x],x])^2==1/(x^2*y[x]^3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (\frac {5}{2}\right )^{2/5} (-\log (x)+c_1){}^{2/5}\\ y(x)&\to \left (\frac {5}{2}\right )^{2/5} (\log (x)+c_1){}^{2/5} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**2 - 1/(x**2*y(x)**3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out