29.19.21 problem 534

Internal problem ID [5130]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 534
Date solved : Sunday, March 30, 2025 at 06:43:07 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.220 (sec). Leaf size: 41

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

\begin{align*} y &= \frac {c_1 \left (c_1 -\sqrt {x^{4}+c_1^{2}}\right )}{x} \\ y &= \frac {c_1 \left (c_1 +\sqrt {x^{4}+c_1^{2}}\right )}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.861 (sec). Leaf size: 73

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

\begin{align*} y(x)\to \frac {x^4}{-x+\frac {\sqrt {1+c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to -\frac {x^4}{x+\frac {\sqrt {1+c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x**3 - y(x))*y(x)/(x*(x**3 + y(x))) cannot be solved by the factorable group method