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Question

If z=z(x) and (2+cosx)dzdx+(sinx)z=sinx, z(x)>0 and z(π2)=3, then z(π3) is 
  1. 72
  2. 32
  3. 52
  4. 12


Solution

The correct option is A 72
(2+cosx)dzdx+(sinx)z=sinx(2+cosx)dzdx=(z1)sinxdzz1=sinx2+cosx dx
Integrating
ln|z1|=ln|2+cosx|+C
It is given z(π2)=3
ln2=ln2+CC=0
When x=π3
ln|z1|=ln52z=72

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