88.7.12 problem 12

Internal problem ID [24007]
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 : 12
Date solved : Thursday, October 02, 2025 at 09:53:43 PM
CAS classification : [_rational]

\begin{align*} 2 x^{2} y-y^{2}+6 x^{3} y^{3}+\left (2 x^{4} y^{2}-x^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 67

ode:=2*x^2*y(x)-y(x)^2+6*x^3*y(x)^3+(2*x^4*y(x)^2-x^3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {c_1 +\ln \left (x \right )+\sqrt {-8 x^{5}+\ln \left (x \right )^{2}+2 c_1 \ln \left (x \right )+c_1^{2}}}{4 x^{3}} \\ y &= \frac {c_1 +\ln \left (x \right )-\sqrt {-8 x^{5}+\ln \left (x \right )^{2}+2 c_1 \ln \left (x \right )+c_1^{2}}}{4 x^{3}} \\ \end{align*}

✓ Mathematica. Time used: 0.462 (sec). Leaf size: 88

ode=( 2*x^2*y[x]-y[x]^2+6*x^3*y[x]^3 )+( 2*x^4*y[x]^2-x^3  )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-\sqrt {-8 x^5+\log ^2(x)+2 c_1 \log (x)+c_1{}^2}+\log (x)+c_1}{4 x^3}\\ y(x)&\to \frac {\sqrt {-8 x^5+\log ^2(x)+2 c_1 \log (x)+c_1{}^2}+\log (x)+c_1}{4 x^3}\\ y(x)&\to 0 \end{align*}

✗ Sympy

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

Timed Out