40.3.32 problem 26 (f)

Internal problem ID [6636]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 26 (f)
Date solved : Sunday, March 30, 2025 at 11:13:02 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.414 (sec). Leaf size: 30

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

\[ y = \frac {\operatorname {RootOf}\left (c_1 \,\textit {\_Z}^{12}+4 c_1 \,\textit {\_Z}^{3}-x^{3}\right )^{9}+4}{x^{3}} \]

✓ Mathematica. Time used: 60.292 (sec). Leaf size: 1175

ode=(3*x^2*y[x]^2)+4*(x^3*y[x]-3)*D[y[x],x]==0; 
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(3*x**2*y(x)**2 + (4*x**3*y(x) - 12)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out