78.3.18 problem 6 (a)

Internal problem ID [18121]
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 (a)
Date solved : Tuesday, January 28, 2025 at 11:29:15 AM
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: 0.006 (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: 0.184 (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*}