Question

Assertion: Degree of the differential equation: `a(dy/dx)^2 + bdx/dy = c`, is 3

Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.

Which of the following is correct?

विकल्प

• Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

• Assertion is true and Reason is false.

• Assertion is false and Reason is true.

Answer 1

Assertion is false and Reason is true.

Explanation:

Assertion: The degree of a differential equation is defined only if the equation is a polynomial equation in derivatives and their exponents are integers.

The given differential equation is:

 `a(dy/dx)^2 + bdx/dy = c`

1. The term `(dy/dx)^2` is a polynomial in `dy/dx` with degree 2.
2. The term `dx/dy` can be rewritten as `(dy/dx)^-1`, which is not a polynomial in `dy/dx`.

Because `dx/dy` is not a polynomial term in `dy/dx` the degree of the differential equation is not defined in the traditional sense.

Therefore, the assertion that the degree of the differential equation is 3 is false.

Reason: It correctly defines the degree of a differential equation.