23.2.330 problem 359

Internal problem ID [5685]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 359
Date solved : Tuesday, September 30, 2025 at 01:57:29 PM
CAS classification : [_rational]

\begin{align*} x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right )&=a^{2} \end{align*}

✗ Maple

ode:=x^2*(diff(y(x),x)^6+3*y(x)^4+3*y(x)^2+1) = a^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^2* ( (D[y[x],x])^6 +3* (y[x])^4 +3 *(y[x])^2 + 1)==a^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a**2 + x**2*(3*y(x)**4 + 3*y(x)**2 + Derivative(y(x), x)**6 + 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out