Question

Assume that y(x) = 5-x^2 and y(x) = x sin(2x) are solutions of a linear, homogeneous differential equation with constant real coefficients.


Q1). The order of the differential equation could be equal to 5 ?

Q2) the order of the differential equation is greater than or equal to 7?

Q3) the characteristics equation has repeated roots?

Q4). 0 is definitely a root of the characteristics equation ?

Q5) 1-2i is definitely a root of the characteristics equation ?