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Differential Equations question

2024 · 8 Apr · Shift 1 · Q39

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JEE Main
Mathematics
Differential Equations
2024 · 8 Apr · Shift 1 · Q39

Differential Equations question

2024 · 8 Apr · Shift 1 · Q39

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

y=y(x)

be the solution of the differential equation

(1+y^2) e^{\tan x} d x+\cos ^2 x(1+e^{2 \tan x}) d y=0, y(0)=1

. Then

y\left(\frac{\pi}{4}\right)

is equal to

A
$\frac{1}{e^2}$
B
$\frac{2}{e^2}$
C
$\frac{2}{e}$
D
$\frac{1}{e}$

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