Question

Integrating factor of the differential equation \[ \frac{dy}{dx} + y = \frac{x^3 + y}{x} \]

• A. \( \frac{x}{e^x} \)
• B. \( e^x \)
• C. \( \frac{e^x}{x} \)
• D. \( x e^{x^2} \)

Hint:

For first-order linear differential equations, the integrating factor is calculated using the formula \( I.F. = e^{\int P(x) \, dx} \), where \( P(x) \) is the coefficient of \( y \) in the equation.

Answer 1

The Correct Option is C