Question

What function (or functions) do you know from calcu-
lus is such that its second derivative is itself? Its second
derivative is the negative of itself? Write each answer in
the form of a second-order differential equation with a
solution.

Answer 1

can you think of a function that does not change upon taking the derivative?

Answer 2

Think "transcendental functions"

Answer 3

\[y=\exp(x)\]

Answer 4

"Its second derivative is the negative of itself?"

Think trig.