23.1.559 problem 549

Internal problem ID [5166]
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 : 549
Date solved : Tuesday, September 30, 2025 at 11:47:20 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 63

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

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

✓ Mathematica. Time used: 0.392 (sec). Leaf size: 75

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

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

✗ Sympy

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

Timed Out