Question

If $y = P \cos(ux) + Q \sin(ux)$, where $P, Q,$ and $u$ are constants, show that $\frac{d^2y}{dx^2} + u^2y = 0$.

Hint:

When differentiating sine and cosine functions repeatedly, remember that the signs alternate in pairs: sine becomes cosine, cosine becomes negative sine, negative sine becomes negative cosine, and negative cosine returns to positive sine.

Answer 1