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Q.

If dydx+ysec⁡x=tan⁡x then (2+1)yπ4−y(o)=

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a

2−π4

b

2+π4

c

2−π2

d

2+π2

answer is A.

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Detailed Solution

I. F=exp⁡∫sec⁡xdx=sec⁡x+tan⁡x y(sec⁡x+tan⁡x)=∫tan⁡x(sec⁡x+tan⁡x)=sec⁡x+tan⁡x−x+cx=π4→(2+1)yπ4=2+1−π4+cx=0→y(0)=1+c⇒(2+1)yπ4−y(0)=2−π4
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