88.5.2 problem 2

Internal problem ID [23976]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 35
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:48:26 PM
CAS classification : [`x=_G(y,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=(2*x^3*y[x])+(2*x^2*y[x]^2+2*y[x]^4+Log[y[x]] )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE 2*x**3*y(x)/(2*x**2*y(x)**2 + 2*y(x)**4 + log(y(x))) + Derivativ