50.5.17 problem 5(b)

Internal problem ID [7887]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 5(b)
Date solved : Monday, January 27, 2025 at 03:31:03 PM
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: 0.005 (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: 3.726 (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*}