Answer :

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.


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