The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants will be:

Which of the following differential equations has $y=x$ as one of its particular solutions?

The differential equation of the family of curves $y = a \cos(x + b)$ is

For each of the exercises given below,verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
$y=e^{x}(a \cos x+b \sin x) \quad: \frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0$

The differential equation corresponding to the family of curves $y=e^x(A \cos x+B \sin x)$ is

The differential equation of $y = A{e^{2x}} + B{e^{ - 2x}}$ is (where $A$ and $B$ are arbitrary constants):