34.3.32 problem 26 (f)

Internal problem ID [7923]
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 : Tuesday, September 30, 2025 at 05:10:07 PM
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: 0.199 (sec). Leaf size: 96

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]
 

\[ \text {Solve}\left [70^{2/3} \left (-\frac {1}{x^3}\right )^{2/3} x^2 \log (x)+12 c_1=12 \int _1^{\frac {\left (-\frac {1}{x^3}\right )^{2/3} x^2 \left (2 x^3 y(x)-15\right )}{\sqrt [3]{70} \left (x^3 y(x)-3\right )}}\frac {1}{K[1]^3+\frac {39 \sqrt [3]{-1} K[1]}{70^{2/3}}+1}dK[1],y(x)\right ] \]

✗ 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