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Differential Equations question

2024 · 6 Apr · Shift 1 · Q46

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JEE Main
Mathematics
Differential Equations
2024 · 6 Apr · Shift 1 · Q46

Differential Equations question

2024 · 6 Apr · Shift 1 · Q46

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

y=y(x)

be the solution of the differential equation

\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}

,

y(1)=0

. Then

y(0)

is

A
$\frac{1}{4}\left(e^{\pi / 2}-1\right)$
B
$\frac{1}{2}\left(1-e^{\pi / 2}\right)$
C
$\frac{1}{4}\left(1-e^{\pi / 2}\right)$
D
$\frac{1}{2}\left(e^{\pi / 2}-1\right)$

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