78.5.7 problem 2 (g)

Internal problem ID [18150]
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 : 2 (g)
Date solved : Tuesday, January 28, 2025 at 11:34:12 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x +3 y^{2}+2 x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(( x+3*y(x)^2 ) +( 2*x*y(x)  )*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {-x \left (x^{4}-4 c_1 \right )}}{2 x^{2}} \\ y &= \frac {\sqrt {-x \left (x^{4}-4 c_1 \right )}}{2 x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.210 (sec). Leaf size: 55

DSolve[( x+3*y[x]^2 )+( 2*x*y[x] )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-x^4+4 c_1}}{2 x^{3/2}} \\ y(x)\to \frac {\sqrt {-x^4+4 c_1}}{2 x^{3/2}} \\ \end{align*}