23.1.706 problem 702

Internal problem ID [5313]
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 : 702
Date solved : Tuesday, September 30, 2025 at 12:29:21 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4}&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 34

ode:=(5*x-y(x)-7*y(x)^3*x)*diff(y(x),x)+5*y(x)-y(x)^4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x +\frac {\frac {y^{5}}{5}-\frac {5 y^{2}}{2}-c_1}{y \left (y^{3}-5\right )^{2}} = 0 \]

✓ Mathematica. Time used: 5.136 (sec). Leaf size: 132

ode=(5 x-y[x]-7 x y[x]^3)D[y[x],x]+5 y[x]-y[x]^4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x=\exp \left (\int _1^{y(x)}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ) \int _1^{y(x)}\frac {\exp \left (-\int _1^{K[2]}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ) K[2]}{5 K[2]-K[2]^4}dK[2]+c_1 \exp \left (\int _1^{y(x)}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-7*x*y(x)**3 + 5*x - y(x))*Derivative(y(x), x) - y(x)**4 + 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out