47.3.1 problem 1

Internal problem ID [7474]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.3. Exact equations problems. page 24
Problem number : 1
Date solved : Sunday, March 30, 2025 at 12:09:52 PM
CAS classification : [_exact, _rational]

\begin{align*} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 125

ode:=x*(2-9*x*y(x)^2)+y(x)*(4*y(x)^2-6*x^3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {6 x^{3}-2 \sqrt {9 x^{6}-4 x^{2}-4 c_1}}}{2} \\ y &= \frac {\sqrt {6 x^{3}-2 \sqrt {9 x^{6}-4 x^{2}-4 c_1}}}{2} \\ y &= -\frac {\sqrt {6 x^{3}+2 \sqrt {9 x^{6}-4 x^{2}-4 c_1}}}{2} \\ y &= \frac {\sqrt {6 x^{3}+2 \sqrt {9 x^{6}-4 x^{2}-4 c_1}}}{2} \\ \end{align*}

✓ Mathematica. Time used: 5.859 (sec). Leaf size: 163

ode=x*(2-9*x*y[x]^2)+y[x]*(4*y[x]^2-6*x^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {\sqrt {3 x^3-\sqrt {9 x^6-4 x^2+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {3 x^3-\sqrt {9 x^6-4 x^2+4 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {3 x^3+\sqrt {9 x^6-4 x^2+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {3 x^3+\sqrt {9 x^6-4 x^2+4 c_1}}}{\sqrt {2}} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(-9*x*y(x)**2 + 2) + (-6*x**3 + 4*y(x)**2)*y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out