23.1.383 problem 368

Internal problem ID [4990]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 368
Date solved : Tuesday, September 30, 2025 at 09:12:23 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 x^{3} y^{\prime }&=\left (x^{2}-y^{2}\right ) y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

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

\begin{align*} y &= \frac {x}{\sqrt {c_1 x -1}} \\ y &= -\frac {x}{\sqrt {c_1 x -1}} \\ \end{align*}

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to -\frac {x}{\sqrt {-1+c_1 x}}\\ y(x)&\to \frac {x}{\sqrt {-1+c_1 x}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.520 (sec). Leaf size: 29

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

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