88.7.9 problem 9

Internal problem ID [24004]
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 41
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:52:19 PM
CAS classification : [_rational]

\begin{align*} \frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{x^{2} y^{4}+1}&=0 \end{align*}

✗ Maple

ode:=(8*x^4*y(x)+12*x^3*y(x)^2+2)/(2*x+3*y(x))+(2*x^5+3*x^4*y(x)+3)/(1+x^2*y(x)^4)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=( (8*x^4*y[x]+12*x^3*y[x]^2+2)/(2*x+3*y[x]) )+( (2*x^5+3*x^4*y[x]+3)/(1+x^2*y[x]^4)  )*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**5 + 3*x**4*y(x) + 3)*Derivative(y(x), x)/(x**2*y(x)**4 + 1) + (8*x**4*y(x) + 12*x**3*y(x)**2 + 2)/(2*x + 3*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out