Internal problem ID [1057]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 28(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2}+y^{2}+2 y y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve((x^2+y(x)^2)+(2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 c_{1}\right )}}{3 x} \\ y \relax (x ) = \frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 c_{1}\right )}}{3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 60
DSolve[(x^2+y[x]^2)+(2*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ y(x)\to \frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ \end{align*}