`y=c_1 x+c_2 sin(2x+c_3)` (`C_1, C_2, C_3` are arbitrary constants)

The differential equation whose solution is y=c_1 cos ax+c_2 sin ax is (Where c_1,c_2 are arbitrary constants)

Verify that the function y=C_1e^(a x)cosb x+C_2e^(ax)sinb x ,\ C_1, C_2,\ are arbitrary constants is a solution of the differential equation (d^2y)/(dx^2)-2a(dy)/(dx)+(a^2+b^2)y=0

Write the order of the differential equation associated with the primitive y=C_1+C_2e^x+C_3e^(-2x)+C_4,\ w h e r e\ C_1, C_2, C _3,\ C_4 are arbitrary constants.

Write the order of the differential equation associated with the primitive y=C_1+C_2e^x+C_3e^(-2x+C_4),\ w h e r e\ C_1, C_2, C-3,\ C_4 are arbitrary constants.