Find the particular solution of the differential equation : `cos x dy/dx+y sin x =4x cos^2 x,(x ne pi/0)`, given that `y=pi/3,x=pi/6`.

Find the particular solution of the differential equation cos x (dy/dx) + y sin x = 4x cos^2 x, (x ne pi/2) given that y = 3, x = 0

Find the particular solution of the differential equation : sin x dy/dx+y cos x =4x,(x ne 0) , given that y=0,x=pi/2 .

Find the particular solution of the differential equation cos x (dy/dx) = y sin x, y = 1 when x = 0 .

Find the particular solution of the differential equation : cos x dy/dx+y=(4x cos x)/(sec x +tan x ),(x ne pi/2) , given that y=0,x=2 .

Find the particular solution of the differential equation cot x (dy/dx) = y, y = 1 when x = 0 .

Find the particular solution of the differential equation (dy/dx) - 3y cot x = sin 2x, (x ne 0) given that y = 0, x = pi/2 .

Find the particular solution of the differential equation dy/dx -y/x + cosec(y/x) = 0, (x ne 0) , given that y = 0, x =1 .

Find the particular solution of the differential equation : sec^2 x tan y dx- sec^2 y tan x dy=0 , given that y = pi/3,x = pi/6 .