Which of the following statements are true?

I. The order of a differential equation is always a positive integer.

II. The degree of a differential equation is always defined.

III. $\frac{dy}{dx} = \cos x$ has order 1 and degree 1.

IV. Squaring a derivative changes the order of the equation.

Explanation

1. 01

   The order counts derivatives, so it is a positive integer (I); and $\frac{dy}{dx} = \cos x$ is a polynomial of degree 1 in its only derivative (III).

2. 02

   II is false: with a derivative inside $\sin$ or $e^{\;}$, the degree is not defined. IV is false: a power changes the degree, not the order.