The differential equation of the family of all straight lines passing through the origin is

If $m$ and $n$ are respectively the order and the degree of the differential equation representing the family of curves $y^2 - 5ax - 5a^{3/2} = 0$ ($a > 0$ is a parameter), then the value of $m - n$ is

If the differential equation having $y=Ae^x+B \sin x$ as its general solution is $f(x) \frac{d^2 y}{d x^2}+g(x) \frac{d y}{d x}+h(x) y=0$, then $f(x)+g(x)+h(x)=$

Form the differential equation of the family of circles having centre on the $y$-axis and radius $3$ units.

If $c$ is a parameter,then the differential equation of the family of curves $x^2=c(y+c)^2$ is

Find the differential equation for the family of curves $y^{2}=a(b^{2}-x^{2})$ by eliminating the arbitrary constants $a$ and $b$.