Let $$f(x)$$ be a positive function such that the area bounded by $$y = f(x), y = 0$$ from $$x = 0$$ to $$x = a > 0$$ is $$e^{-a} + 4a^2 + a - 1$$. Then the differential equation, whose general solution is $$y = c_1 f(x) + c_2$$, where $$c_1$$ and $$c_2$$ are arbitrary constants, is

A

$$(8e^x - 1)\frac{d^2y}{dx^2} + \frac{dy}{dx} = 0$$

B

$$(8e^x - 1)\frac{d^2y}{dx^2} - \frac{dy}{dx} = 0$$

C

$$(8e^x + 1)\frac{d^2y}{dx^2} - \frac{dy}{dx} = 0$$

D

$$(8e^x + 1)\frac{d^2y}{dx^2} + \frac{dy}{dx} = 0$$