For each of the differential equations given in question, find a particular solution satisfying the given condition:

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 cosec^{3}x = 2cosecx + C

⇒ y =

⇒ y = -2sin^{2}x + Csin^{3}x--------------(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 = -2sin^{2}x + 4sin^{3}x

⇒ y = 4sin^{3}x - 2sin^{2}x

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

y = 4sin^{3}x - 2sin^{2}x.

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