54.2.182 problem 759

Internal problem ID [12056]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 759
Date solved : Sunday, October 12, 2025 at 02:15:00 AM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=-\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y} \end{align*}

✓ Maple. Time used: 0.111 (sec). Leaf size: 247

ode:=diff(y(x),x) = -1/243*I*(54*I*x^2+81*y(x)^4+18*x^4*y(x)^2+x^8)*x/y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 35.844 (sec). Leaf size: 1026

ode=D[y[x],x] == ((-1/243*I)*x*((54*I)*x^2 + x^8 + 18*x^4*y[x]^2 + 81*y[x]^4))/y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**8 + 18*x**4*y(x)**2 + x**2*complex(0, 54) + 81*y(x)**4)*complex(0, 1/243)/y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x*(-x**8 - 18*x**4*y(x)**2 - x**2*complex(0, 54) - 81*y(x)**4)*complex(0, 1/243)/y(x) + Derivative(y(x), x) cannot be solved by the factorable group method