50.5.16 problem 5(a)

Internal problem ID [7886]
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(a)
Date solved : Monday, January 27, 2025 at 03:31:01 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 32

dsolve(diff(y(x),x)=(1-x*y(x)^2)/(2*x^2*y(x)),y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {x \left (\ln \left (x \right )+c_{1} \right )}}{x} \\ y &= -\frac {\sqrt {x \left (\ln \left (x \right )+c_{1} \right )}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.209 (sec). Leaf size: 40

DSolve[D[y[x],x]==(1-x*y[x]^2)/(2*x^2*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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