Question

The integrating factor of the linear differential equation \( \frac{dy}{dx} = \frac{1}{4x + 3y} \) is

• A. \( e^{-4x} \)
• B. \( e^{4x} \)
• C. \( e^{3y} \)
• D. \( e^{-3y} \)

Hint:

When solving linear differential equations, always find the integrating factor by solving for \( P(x) \).

Answer 1

The Correct Option is A

The given linear differential equation is in the form \( \frac{dy}{dx} = \frac{1}{4x + 3y} \). The integrating factor for such an equation is \( e^{\int P(x)dx} \), where \( P(x) \) is the coefficient of \( y \) after the equation is rewritten. After simplification, the integrating factor becomes: \[ e^{-4x} \] Thus, the integrating factor is: \[ \boxed{e^{-4x}} \]