Question

Which equation is satisfied by \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\]?

Options

• \[\frac{d^2y}{dx^2}+y=0\]

• \[\frac{d^2y}{dx^2}+\frac{dy}{dx}=0\]

• \[\frac{d^2y}{dx^2}-y=0\]

• \[\frac{dy}{dx}+y=0\]

Answer 1

For this function, \[\frac{d^2y}{dx^2}=-y\]. Adding \[y\] to both sides gives \[\frac{d^2y}{dx^2}+y=0\].