The differential equation of the family of curves $y = ax + \frac{1}{a}$, where $a (\neq 0)$ is an arbitrary constant, has the degree

The differential equation for which $y = ax^2 + bx + c$ is the general solution is:

If $c$ and $d$ are arbitrary constants,then $y=e^{2 x}(\cosh \sqrt{2} x+d \sinh \sqrt{2} x)$ is the general solution of the differential equation

$f(x, y, c_1, c_2) = 0$ is an equation containing two arbitrary constants $c_1$ and $c_2$. If the differential equation having $f(x, y, c_1, c_2) = 0$ as its general solution is of $k^{\text{th}}$ order, then the differential equation corresponding to $x^k + y^k = c^2$ ($c$ is an arbitrary constant) is

The differential equation of the family of curves ${y^2} = 4a(x + a)$,where $a$ is an arbitrary constant,is

Form the differential equation of the family of circles touching the $y$-axis at the origin.