JEE Advanced Model Paper 20 with solutions for online practice

Given equation is dydx + 2ytanx = sinx
I.F. is e

2sinxdx

∫

= sec2x
∴ solutions y . sec2x = ∫ sinx . sec2 x dx + C
⇒ y . sec2x = sec x + c , if it is passes through (

π

3

,0)
C = - 2 , ∴ y sec2x = sec x - 2 or
y = cos x - 2 cos2x = cosx - 1 - cos 2 x

d2y

dx2

> 0 when x = 0 , or x = π ,

d2y

dx2

< 0 when cos x = 1/4
∴ local min = –1, –3, local maximum

1

4

−

2

16

=

1

8

Period of the function is 2π.