23.1.662 problem 657

Internal problem ID [5269]
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 : 657
Date solved : Tuesday, September 30, 2025 at 12:06:14 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (1-4 x +3 x y^{2}\right ) y^{\prime }&=\left (2-y^{2}\right ) y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=(1-4*x+3*x*y(x)^2)*diff(y(x),x) = (2-y(x)^2)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ x +\frac {1}{y^{2}}-\frac {c_1}{\sqrt {y^{2}-2}\, y^{2}} = 0 \]

✓ Mathematica. Time used: 0.178 (sec). Leaf size: 130

ode=(1-4 x+3 x y[x]^2)D[y[x],x]==(2-y[x]^2)y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x=\exp \left (\int _1^{y(x)}\frac {3 K[1]^2-4}{2 K[1]-K[1]^3}dK[1]\right ) \int _1^{y(x)}\frac {\exp \left (-\int _1^{K[2]}\frac {3 K[1]^2-4}{2 K[1]-K[1]^3}dK[1]\right )}{2 K[2]-K[2]^3}dK[2]+c_1 \exp \left (\int _1^{y(x)}\frac {3 K[1]^2-4}{2 K[1]-K[1]^3}dK[1]\right ),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((y(x)**2 - 2)*y(x) + (3*x*y(x)**2 - 4*x + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out