Differential Equations_JEE-Main 080424_(S1) - Competishun – Live JEE & NEET Courses and Exam Prep

JEE MAIN 2024

08-04-24 S1

Question

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 $\mathrm{e}^{-\mathrm{a}}+4 \mathrm{a}^2+\mathrm{a}-1$. 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:

Select the correct option:

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

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

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

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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution