23.1.704 problem 700

Internal problem ID [5311]
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 : 700
Date solved : Tuesday, September 30, 2025 at 12:29:16 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.199 (sec). Leaf size: 28

ode:=x*(x^4-2*y(x)^3)*diff(y(x),x)+(2*x^4+y(x)^3)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (x \right )-c_1 +\frac {3 \ln \left (\frac {y \left (-2 x^{4}+y^{3}\right )}{x^{{16}/{3}}}\right )}{10} = 0 \]

✓ Mathematica. Time used: 60.097 (sec). Leaf size: 1139

ode=x(x^4-2 y[x]^3)D[y[x],x]+(2 x^4+y[x]^3)y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 94.143 (sec). Leaf size: 1465

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

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