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Differential Equations question

2023 · 29 Jan · Shift 2 · Q24

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JEE Main
Mathematics
Differential Equations
2023 · 29 Jan · Shift 2 · Q24

Differential Equations question

2023 · 29 Jan · Shift 2 · Q24

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

y=y(x)

be the solution of the differential equation

x{\log _e}x{{dy} \over {dx}} + y = {x^2}{\log _e}x,(x \gt 1)

. If

y(2) = 2

, then

y(e)

is equal to

A
${{1 + {e^2}} \over 2}$
B
${{1 + {e^2}} \over 4}$
C
${{2 + {e^2}} \over 2}$
D
${{4 + {e^2}} \over 4}$

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