23.2.176 problem 180

Internal problem ID [5531]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 180
Date solved : Tuesday, September 30, 2025 at 12:51:24 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 37

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

\begin{align*} y &= \frac {c_1 x -2 \sqrt {x a}}{x} \\ y &= \frac {c_1 x +2 \sqrt {x a}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to -\frac {2 \sqrt {a}}{\sqrt {x}}+c_1\\ y(x)&\to \frac {2 \sqrt {a}}{\sqrt {x}}+c_1 \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 31

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

\[ \left [ y{\left (x \right )} = C_{1} + \frac {2 \sqrt {a}}{\sqrt {x}}, \ y{\left (x \right )} = C_{1} - \frac {2 \sqrt {a}}{\sqrt {x}}\right ] \]