Question

For the fundamental solution set S={x, cos x}
can we construct a linear ODE with constant coefficients?

Answer 1

I have found the set to be linearly independent.
The annihilator for the functions are \[D^{2} and (D ^{2} + 1)\]

Is the characteristic equation then \[r ^{4} + r ^{2} = 0\]?

Answer 2

that answer makes sense to me, but I can't say I'm sure...

Answer 3

Well yeah it seems right, but I'm not sure since there are only 2 terms in the solution set, but the equation is of the fourth order.