82.8.1 problem 36-1

Internal problem ID [21872]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 36. Nonlinear differential equations. Page 1203
Problem number : 36-1
Date solved : Thursday, October 02, 2025 at 08:03:08 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 2 x^{4} y y^{\prime }+y^{4}&=4 x^{6} \end{align*}

✓ Maple. Time used: 0.190 (sec). Leaf size: 65

ode:=2*x^4*y(x)*diff(y(x),x)+y(x)^4 = 4*x^6; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\sqrt {\left (x^{5}-c_1 \right ) x \left (x^{5}+4 c_1 \right )}\, x}{-x^{5}+c_1} \\ y &= \frac {\sqrt {\left (x^{5}-c_1 \right ) x \left (x^{5}+4 c_1 \right )}\, x}{x^{5}-c_1} \\ \end{align*}

✓ Mathematica. Time used: 5.632 (sec). Leaf size: 147

ode=2*x^4*y[x]*D[y[x],x]+y[x]^4==4*x^6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt {x^8-4 e^{5 c_1} x^3}}{\sqrt {x^5+e^{5 c_1}}}\\ y(x)&\to \frac {\sqrt {x^8-4 e^{5 c_1} x^3}}{\sqrt {x^5+e^{5 c_1}}}\\ y(x)&\to -2 \sqrt {-x^3}\\ y(x)&\to 2 \sqrt {-x^3}\\ y(x)&\to -\frac {\sqrt {x^8}}{\sqrt {x^5}}\\ y(x)&\to \frac {\sqrt {x^8}}{\sqrt {x^5}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**6 + 2*x**4*y(x)*Derivative(y(x), x) + y(x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out