8.6.33 problem 33 (a)

Internal problem ID [803]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 33 (a)
Date solved : Saturday, March 29, 2025 at 10:29:04 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 x y} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 47

ode:=diff(y(x),x) = 1/4*(-3*x^2-2*y(x)^2)/x/y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {2}\, \sqrt {-x \left (x^{3}-2 c_1 \right )}}{2 x} \\ y &= \frac {\sqrt {2}\, \sqrt {-x \left (x^{3}-2 c_1 \right )}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.215 (sec). Leaf size: 60

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

\begin{align*} y(x)\to -\frac {\sqrt {-x^3+2 c_1}}{\sqrt {2} \sqrt {x}} \\ y(x)\to \frac {\sqrt {-x^3+2 c_1}}{\sqrt {2} \sqrt {x}} \\ \end{align*}

✓ Sympy. Time used: 0.470 (sec). Leaf size: 39

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

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