51.1.56 problem 56

Internal problem ID [10326]
Book : First order enumerated odes
Section : section 1
Problem number : 56
Date solved : Tuesday, September 30, 2025 at 07:19:30 PM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 55

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

\begin{align*} \frac {\sqrt {y x}\, y^{2}-c_1 \sqrt {x}-5 x}{\sqrt {x}} &= 0 \\ \frac {\sqrt {y x}\, y^{2}-c_1 \sqrt {x}+5 x}{\sqrt {x}} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 53

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

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

✓ Sympy. Time used: 164.825 (sec). Leaf size: 891

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

\[ \text {Solution too large to show} \]