78.3.19 problem 6 (b)

Internal problem ID [18122]
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 : Tuesday, January 28, 2025 at 11:29:17 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)=(2+3*x*y(x)^2)/(4*x^2*y(x)),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*}

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==(2+3*x*y[x]^2)/(4*x^2*y[x]),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*}