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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?
Options
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.
Solution
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`
- The term `(dy/dx)^2` is a polynomial in `dy/dx` with degree 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.
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