7.7.33 problem 33

Internal problem ID [211]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 33
Date solved : Tuesday, March 04, 2025 at 11:03:21 AM
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: 0.003 (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: 0.224 (sec). Leaf size: 60

ode=D[y[x],x] == - (3*x^2+2*y[x]^2)/(4*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: 0.486 (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)
 

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