23.1.596 problem 589

Internal problem ID [5203]
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 : 589
Date solved : Tuesday, September 30, 2025 at 11:54:49 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.085 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 60.178 (sec). Leaf size: 1769

ode=x*(3+2*x^2*y[x])*D[y[x],x]+(4+3*x^2*y[x])*y[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*(2*x**2*y(x) + 3)*Derivative(y(x), x) + (3*x**2*y(x) + 4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out