29.13.11 problem 365

Internal problem ID [4965]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 365
Date solved : Sunday, March 30, 2025 at 04:24:01 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: 0.003 (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: 0.275 (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: 0.752 (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)
 

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