Internal problem ID [5478]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x +3 y^{2}+2 x y y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 43
dsolve((x+3*y(x)^2)+(2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {x \left (-x^{4}+4 c_{1}\right )}}{2 x^{2}} \\ y \relax (x ) = \frac {\sqrt {x \left (-x^{4}+4 c_{1}\right )}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.281 (sec). Leaf size: 55
DSolve[(x+3*y[x]^2)+(2*x*y[x])*y'[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*}