78.5.23 problem 4 (L)

Internal problem ID [18166]
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 9 (Integrating Factors). Problems at page 80
Problem number : 4 (L)
Date solved : Tuesday, January 28, 2025 at 11:35:52 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} 2 x y^{2}-y+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve((2*x*y(x)^2-y(x))+x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {x}{x^{2}+c_1} \]

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 20

DSolve[(2*x*y[x]^2-y[x])+x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{x^2+c_1} \\ y(x)\to 0 \\ \end{align*}