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Question

If cosxdydxysinx=6x, (0<x<π2) and y(π3)=0, then y(π6) is equal to :
  1. π22
  2. π223
  3. π243
  4. π223


Solution

The correct option is B π223
cosxdydxysinx=6x,  (0<x<π2)
dydx(tanx) y=6xsecx

I.F.=etanx dx=eln(cosx)=cosx

cosx×y=6x dx+C
ycosx=3x2+C
y=3x2secx+Csecx
As y(π3)=0C=π23

y=(3x2π23)secx

y(π3)=(3π236π23)×23=π223

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