23.1.595 problem 588

Internal problem ID [5202]
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 : 588
Date solved : Tuesday, September 30, 2025 at 11:54:47 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

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

\begin{align*} y &= \frac {3+\sqrt {-8 x^{3}+4 c_1 x +9}}{2 x^{2}} \\ y &= \frac {3-\sqrt {-8 x^{3}+4 c_1 x +9}}{2 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.544 (sec). Leaf size: 71

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

\begin{align*} y(x)&\to -\frac {-3 x+\sqrt {x^2 \left (-8 x^3+4 c_1 x+9\right )}}{2 x^3}\\ y(x)&\to \frac {3 x+\sqrt {x^2 \left (-8 x^3+4 c_1 x+9\right )}}{2 x^3} \end{align*}

✗ Sympy

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

Timed Out