15.8.34 problem 36

Internal problem ID [3037]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 36
Date solved : Sunday, March 30, 2025 at 01:13:09 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 43

ode:=y(x)*(3*x^2+y(x))-x*(x^2-y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x^{2} \left (\operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{4}-c_1 \textit {\_Z} +3 x \right )^{3}-1\right )}{3 \operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{4}-c_1 \textit {\_Z} +3 x \right )^{3}} \]

✓ Mathematica. Time used: 60.143 (sec). Leaf size: 1665

ode=y[x]*(3*x^2+y[x])-x*(x^2-y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (3*x**2 + y(x))*y(x)/(x*(x**2 - y(x))) cannot be solved by the factorable group method