29.23.23 problem 654

Internal problem ID [5245]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 654
Date solved : Sunday, March 30, 2025 at 07:30:50 AM
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: 60.2 (sec). Leaf size: 2348

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]
 

Too large to display

✗ 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