The differential equation of all circles of radius $a$ is of order:

The differential equation whose solution is $Ax^2 + By^2 = 1$,where $A$ and $B$ are arbitrary constants,is of

The differential equation obtained by eliminating the arbitrary constants $a$ and $b$ from $xy = ae^x + be^{-x}$ is

If $Ax^3+Bxy=4$ (where $A$ and $B$ are arbitrary constants) is the general solution of the differential equation $F(x) \frac{d^2 y}{d x^2}+G(x) \frac{d y}{d x}-2 y=0$,then $F(1)+G(1)=$

The differential equation of the family of all parabolas whose axis is the $y$-axis is ...

The differential equation whose general solution is given by $y = (c_1 \cos(x + c_2)) - (c_3 e^{(-x + c_4)}) + (c_5 \sin x)$,where $c_1, c_2, c_3, c_4, c_5$ are arbitrary constants,is