If y = y(x) is the solution... | Differential Equations JEE Main 2021

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JEE MAIN 2021

16-03-2021 S2

Question

If $y=y(x)$ is the solution of the differential equation $\frac{d y}{d x}+(\tan x) y=\sin x, 0 \leq x \leq \frac{\pi}{3}$, with $y(0)=0$, then $y\left(\frac{\pi}{4}\right)$ equal to :

Select the correct option:

A

$\frac{1}{4} \log _{\mathrm{e}} 2$

B

$\left(\frac{1}{2 \sqrt{2}}\right) \log _e 2$

C

$\log _{\mathrm{e}} 2$

D

$\frac{1}{2} \log _{\mathrm{e}} 2$

✓ Correct! Well done.

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