It is given that

This is equation in the form of (where, p = -3cotx and Q = sin2x)

Now, I.F. =

Thus, the solution of the given differential equation is given by the relation:

y(I.F.) =

⇒ y cosec³x = 2cosecx + C

⇒ y =

⇒ y = -2sin²x + Csin³x--------------(1)

Now, it is given that y = 2 when x =

Thus, we get,

2 = -2 + C

⇒ C = 4

Now, Substituting the value of C = 4 in (1), we get,

y = -2sin²x + 4sin³x

⇒ y = 4sin³x - 2sin²x

Therefore, the required general solution of the given differential equation is

y = 4sin³x - 2sin²x.