Let f(x) be a positive function such that the area bounded by y =… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 8 April, Shift 1Linear Differential Equations

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

Answer & step-by-step solution

Practice more Linear Differential Equations questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step - free to start.

Start free trial More on Linear Differential Equations

Answer & step-by-step solution

Practice more Linear Differential Equations questions

Related questions