50.6.7 problem 1(g)

Internal problem ID [7899]
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 1.8. Integrating Factors. Page 32
Problem number : 1(g)
Date solved : Monday, January 27, 2025 at 03:31:37 PM
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: 0.007 (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: 0.239 (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*}