Question

The general solution of the differential equation $x^3 \frac{dy}{dx} + 3x^2 y = \cos x$ is

• A. $y = \frac{\sin x}{x^3} + C$
• B. $y = \frac{\sin x}{x^3} + Cx$
• C. $y = \frac{\sin x}{x^2} + C$
• D. $y = \frac{\sin x + C}{x^2}$
• E. $y = \frac{\sin x + C}{x^3}$

Hint:

Before using general methods for linear differential equations (like finding an Integrating Factor), check if the LHS is already the exact derivative of a product. In this case, $x^3$ was already the integrating factor.

Answer 1

Answer: (E)