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Differential Equations question

2021 · 26 Aug · Shift 1 · Q24

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JEE Main
Mathematics
Differential Equations
2021 · 26 Aug · Shift 1 · Q24

Differential Equations question

2021 · 26 Aug · Shift 1 · Q24

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let y = y(x) be a solution curve of the differential equation

(y + 1){\tan ^2}x\,dx + \tan x\,dy + y\,dx = 0

,

x \in \left( {0,{\pi \over 2}} \right)

. If

\mathop {\lim }\limits_{x \to 0 + } xy(x) = 1

, then the value of

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

is :

A
$- {\pi \over 4}$
B
${\pi \over 4} - 1$
C
${\pi \over 4} + 1$
D
${\pi \over 4}$

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