What is the number of arbitrary constants in the general solution of a differential equation of order 2?

What is the number of arbitrary constants in the particular solution of a differential equation of order 3?

Find the general solution of cos^2 3theta=0

Find the general solution of sin(3theta)/2=0 .

Find the general solution of the trigonometric equation 2 sin theta+1=0

Find the general solution of the trigonometric equation sqrt(3) sec 2theta=2

Verify that y=A cos x-B sin x is a solution of the differential equation (d^(2)y)/(dx^(2))+y=0

Mention the order and the degree of the differential equation y_3+ky_2 = 0

Mention the order and the degree of the differential equation y_2=root3(y+y_1^2)