6.6.1 problem 1

Internal problem ID [1680]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:59:06 AM
CAS classification : [_separable]

\begin{align*} 6 x^{2} y^{2}+4 x^{3} y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 39

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

\begin{align*} y &= 0 \\ y &= -\frac {\sqrt {2}\, \sqrt {-c_1 x}}{2 x^{2}} \\ y &= \frac {\sqrt {2}\, \sqrt {-c_1 x}}{2 x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to 0\\ y(x)&\to \frac {c_1}{x^{3/2}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = \frac {C_{1}}{x^{\frac {3}{2}}} \]