Name and application of a nonlinear ODE Is there a name for an ODE taking form:
\begin{equation}
\left(\frac{dy}{dx}\right)^2 + a y = 0,
\end{equation}
and if there is, what is the constant `a' called either generally or in certain applications if there are any?
I've searched online for equations of this form, and it seems a specific form of Chrystal's equation
\begin{equation}
\left(\frac{dy}{dx}\right)^2 + bx \frac{dy}{dx} + ay + cx^2 = 0
\end{equation}
takes this form when $b=c=0$.
I would also like to know if there are any physical applications that use this particular type (or a vectorized version) of this ODE.

Let $a= -1/f$; the equation
$$\left(\dfrac{dy}{dx}\right)^2 + a y; \quad  \left(\dfrac{dy}{dx}\right)^2 - \dfrac{y}{f} = 0 \tag1 $$
is called simple harmonic motion and can be  be parametrized
$$ x= 2 ft, y=f t^2$$
so that $a$ is related to max curvature of a parabola at its vertex.
$$ \dfrac{1}{R} =\dfrac{1}{2f}=\dfrac{-a}{2}\tag2 $$
