Mathematics · 2023
JEE Main · 15 April 2023, Shift 1 · Q11
Let x=x(y) be the solution of the differential equation 2(y+2) log_e(y+2) d x+(x+4-2 log_e(y+2)) d y=0, y>-1 with x(e^4-2)=1. Then x(e^9-2) is equal…
Let $\displaystyle x=x(y)$ be the solution of the differential equation
$$2(y+2) \log _e(y+2) d x+\left(x+4-2 \log _e(y+2)\right) d y=0, y>-1
$$
with $\displaystyle x\left(e^4-2\right)=1$. Then $\displaystyle x\left(e^9-2\right)$ is equal to
Official answer
From NTA’s final answer key for this paper.
(4)
$\displaystyle \frac{32}{9}$
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JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.