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.

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.

turingtest · Answer

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

anonymous · Answer

Think "transcendental functions"

anonymous · Answer

$$y=\exp(x)$$

anonymous · Answer

"Its second derivative is the negative of itself?"

Think trig.