78.3.19 problem 6 (b)

Internal problem ID [18051]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 6 (b)
Date solved : Monday, March 31, 2025 at 05:00:08 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

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

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

\begin{align*} y &= -\frac {\sqrt {5}\, \sqrt {5 x^{{7}/{2}} c_1 -2 x}}{5 x} \\ y &= \frac {\sqrt {5}\, \sqrt {5 x^{{7}/{2}} c_1 -2 x}}{5 x} \\ \end{align*}

✓ Mathematica. Time used: 3.693 (sec). Leaf size: 51

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

\begin{align*} y(x)\to -\sqrt {-\frac {2}{5 x}+c_1 x^{3/2}} \\ y(x)\to \sqrt {-\frac {2}{5 x}+c_1 x^{3/2}} \\ \end{align*}

✓ Sympy. Time used: 0.378 (sec). Leaf size: 46

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {5} \sqrt {C_{1} x^{\frac {3}{2}} - \frac {2}{x}}}{5}, \ y{\left (x \right )} = \frac {\sqrt {5} \sqrt {C_{1} x^{\frac {3}{2}} - \frac {2}{x}}}{5}\right ] \]