Question

The solution of the differential equation \( (x + 1)\frac{dy}{dx} - y = e^{3x}(x + 1)^2 \) is:

• A. \( y = (x + 1)e^{3x} + C \)
• B. \( 3y = (x + 1) + e^{3x} + C \)
• C. \( \frac{3y}{x+1} = e^{3x} + C \)
• D. \( ye^{-3x} = 3(x + 1) + C \)

Hint:

For linear first-order differential equations, always start by finding the integrating factor and multiplying through to solve.