Internal problem ID [6325]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 35.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{2}+\frac {2}{x}+2 x y y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 42
dsolve((y(x)^2+2/x)+2*y(x)*x*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-x \left (2 \ln \relax (x )-c_{1}\right )}}{x} \\ y \relax (x ) = -\frac {\sqrt {-x \left (2 \ln \relax (x )-c_{1}\right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.314 (sec). Leaf size: 44
DSolve[(y[x]^2+2/x)+2*y[x]*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-2 \log (x)+c_1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {-2 \log (x)+c_1}}{\sqrt {x}} \\ \end{align*}