Question

If the I.F. of the differential equation \[ \frac{dy}{dx} + 5y = \cos x \sin x e^{Adx}, \text{ then } A = \]

• A. 0
• B. 1
• C. 3
• D. 5

Hint:

For linear first-order differential equations, the integrating factor is used to solve for the general solution.

Answer 1

The Correct Option is A

Step 1: The equation is a first-order linear differential equation. The integrating factor is given by: \[ I.F = e^{\int 5 \, dx} = e^{5x}. \] Step 2: Comparing with the given equation, \( A = 0 \).

Final Answer: \[ \boxed{0} \]