I donot know whether there is actually a zero-order derivative equation, where the equation is defined as having two sides with equality or inequality sign between them. If the question is about a zero-order derivative function, then the answer is yes, since the zero order derivative is the function itself.
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However, as far as we can talk about the differential equation- there is no meaning of "Zero Degree" but as many times while using expansion of differential operator using binomial theorem or while using Leibnitz's rule of differentiation, we simply denote derivatives of zero degree for no differentiation, we can say, for understanding, tha the equations without derivatives eg. y =mx can be treated as Differential Equation of Zero Order.
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You didn't specify the equation. A minimum or maximum value of a function is often found by calculating the derivative of a function, writing an equation for derivative equal to zero, and then analyzing points where the derivative either doesn't exist, or is equal to zero. You'll find find information about this in introductory calculus books.
The derivative of 40 is zero. The derivative of any constant is zero.
Zero. In general, the derivative of any constant is zero.
The "double prime", or second derivative of y = 5x, equals zero. The first derivative is 5, a constant. Since the derivative of any constant is zero, the derivative of 5 is zero.
zero