The order of the differential equation whose solution is $y=a \cos x+b \sin x+c e^{-x}$ is

The order of the differential equation whose general solution is given by $y = (C_1 + C_2) \sin (x + C_3) - C_4 e^{x + C_5}$ is (where $C_1, C_2, C_3, C_4, C_5$ are arbitrary constants).

The differential equation of all circles touching the $Y$-axis at the origin and having their center on the $X$-axis is:

If $a$ and $b$ are arbitrary constants,then the differential equation having $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ as its general solution is

The differential equation of $y=e^x(a+bx+x^2)$ is

The differential equation formed by eliminating $a$ and $b$ from the equation $y=a e^{2 x}+b x e^{2 x}$ is