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Let y=y(x) be the solution of the differ...

Let y=y(x) be the solution of the differential equation,
`dy/dx+y tan x=2x+x^(2)tanx, x in(-pi/2,pi/2),` such that
y(0)= 1. Then

A

`y'((pi)/(4 ) ) - y' (-(pi)/(4) )=pi - sqrt(2)`

B

`Y((pi ) /(4)) - Y (-(pi)/(4) ) = sqrt(2)`

C

` Y ((pi)/(4)) + Y (-(pi)/(4))=(pi^2)/(2) +2`

D

`y' ((pi)/(4))+Y'( -(pi)/( 4))= sqrt(2)`

Text Solution

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The correct Answer is:
A
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