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Let y=y(x) be the solution of the D.E sin⁡xdydx+ycos⁡x=4x,x∈(0,π). If ⇒y(π/2)=0 then y(π/6) is

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a

-49π2

b

493π2

c

-893π2

d

-89π2

answer is D.

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Detailed Solution

∫d(ysinx)=∫4x⇒ysinx=2x2+c passes through (π2,0)⇒c=−π22 ysinx =2x2−π22⇒ put x=π6⇒y2=2⋅π236−π22⇒y=−8π29

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