Question

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A) : For a differential equation x + ax = b for a≠0 , F(x)=x=b-ax and the equilibrium is at $\text{x}=\frac{b}{a}$. This a equilibrium is stable for a > 0. Reason (R) : The equilibrium is obtained for x=b-ax=0 or $\text{x}=\frac{b}{a}$. Stability is obtained when F'(x) is <0. Here F'(x) = -a and so the equilibrium is stable if a> 0.
In the light of the above statements, choose the correct answer from the options given below:

• A. Both (A) and (R) are true and (R) is the correct explanation of (A)
• B. Both (A) and (R) are true but (R) is not the correct explanation of (A)
• C. (A) is true but (R) is false
• D. (A) is false but (R) is true

Answer 1

Answer: (A)

Both (A) and (R) are true and (R) is the correct explanation of (A)

Answer 2

The correct answer is (A) : Both (A) and (R) are true and (R) is the correct explanation of (A)