23.1.578 problem 571

Internal problem ID [5185]
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 : 571
Date solved : Tuesday, September 30, 2025 at 11:51:40 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 47

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

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

✓ Mathematica. Time used: 0.481 (sec). Leaf size: 62

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

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

✗ Sympy

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

Timed Out