29.25.13 problem 710

Internal problem ID [5300]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 710
Date solved : Tuesday, March 04, 2025 at 09:16:56 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 27

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

\[ x -\frac {\left (-y \left (x \right )^{2}+c_{1} \right ) y \left (x \right )^{2}}{2+y \left (x \right )^{3}} = 0 \]

✓ Mathematica. Time used: 60.215 (sec). Leaf size: 2021

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 119.477 (sec). Leaf size: 4383

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

\[ \text {Solution too large to show} \]