If n denotes the degree of a given differential equation, thena)n is a...
See the definition of the degree of a differential equation.
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If n denotes the degree of a given differential equation, thena)n is a...
Differential equations are mathematical equations that involve derivatives of an unknown function. The degree of a differential equation refers to the highest power of the derivative that appears in the equation. In other words, it represents the order of the derivative in the equation.
The given question asks about the possible values of the degree, denoted by 'n', of a differential equation.
a) n is any natural number:
- A natural number is a positive integer (including zero), such as 0, 1, 2, 3, ...
- This option means that the degree of a differential equation can be any positive integer or zero.
- For example, n could be 0, 1, 2, 3, ..., indicating a zeroth-order, first-order, second-order, third-order, ... differential equation.
b) n is any integer:
- An integer includes both positive and negative numbers, such as -3, -2, -1, 0, 1, 2, 3, ...
- This option means that the degree of a differential equation can be any positive or negative integer.
- However, negative degrees are not commonly used in practice as they do not represent meaningful physical situations.
c) n can be zero:
- This option is included in option a, where n can be any natural number, which includes zero.
- A zeroth-order differential equation represents an equation without any derivatives, i.e., it is an algebraic equation.
- For example, if n is 0, the differential equation would not contain any derivatives and could be a simple algebraic equation like 5x + 2 = 0.
d) n is any non-negative integer:
- A non-negative integer includes all natural numbers and zero.
- This option is also included in option a, which allows n to be any natural number, including zero.
Therefore, option a is the most general and correct statement. The degree of a given differential equation can be any natural number, including zero.