​ If y = sin mx, show that ​d^2y/dx^2 + m^2y = 0

Question

If y = sin mx, show that \(\frac{d^2y}{dx^2} + m^2y = 0\)

Answer 1

Given y = sinmx 

\(\frac{dy}{dx}\) = -mcosmx 

\(\frac{d^2y}{dx^2}\) = m²sinmx = -m²y

∴ \(\frac{d^2y}{dx^2}\) + m²y = 0