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 cos x (dy/dx) = y sin x, y = 1 when x = 0 .

Find the particular solution of the differential equation (dy)/dx = -4xy^2 given that y = 1 when x = 0

Find the particular solution of the differential equation e^((dy)/(dx))=a , given that 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 log((dy)/(dx)) = 3x + 4y given that y = 0 when x = 0