JEE MAIN_29-01-2023_S2 - Competishun – Live JEE & NEET Courses and Exam Prep

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JEE Main 2023

29-01-2023_S2

Question

Let $y=y(x)$ be the solution of the differential equation $x \log _e x^{\frac{d y}{d x}}+y=x^2 \log _e x,(x>1)$. If $y(2)=2$, then $\mathrm{y}(\mathrm{e})$ is equal to

Select the correct option:

A

$\frac{4+e^2}{4}$

B

$\frac{1+e^2}{4}$

C

$\frac{2+\mathrm{e}^2}{2}$

D

$\frac{1+\mathrm{e}^2}{2}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

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