76.4.24 problem 30

Internal problem ID [17347]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 30
Date solved : Monday, March 31, 2025 at 03:55:35 PM
CAS classification : [_rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3/y(x)**2 + (3*x/y(x)**2 + 12*y(x))*Derivative(y(x), x) + 12/y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out