Question

Suppose L is the operator defined by Ly=D2y−3Dy+y. Compute L(sin(x)).

Answer 1

Well do you know the 2nd and 1st derivative of sin?

Answer 2

yeah

Answer 3

Well then, what's \(D^2_x \sin x\) and \(D_x \sin x\)?

Answer 4

-sin(x) and cos(x)

Answer 5

so would my answer be: -sin(x) - 3cos(x) + sin(x)?

Answer 6

yes

Answer 7

wow that was way easier than i thought, thank you!

Answer 8

Yeah, the hard part is taking the laplace transform of it!