Question

The integrating factor of \[ \frac{dy}{dx} - y = x^4 - 3x \] \text{is:}

• A. \( x \)
• B. \( \log x \)
• C. \( \frac{1}{x} \)
• D. \( -x \)

Hint:

To find the integrating factor for a linear first-order differential equation, identify the coefficient of \( y \) and integrate it.

Answer 1

The Correct Option is C

The integrating factor for linear differential equations of the form \( \frac{dy}{dx} + P(x)y = Q(x) \) is given by \( e^{\int P(x)dx} \). For this equation, the integrating factor is \( \frac{1}{x} \).
Final Answer: \[ \boxed{\frac{1}{x}} \]