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

1.	If y = sin mx, show that \(\frac{d^2y}{dx^2} + m^2y = 0\)
Answer» Given y = sinmx \(\frac{dy}{dx}\) = -mcosmx \(\frac{d^2y}{dx^2}\) = m²sinmx = -m²y ∴ \(\frac{d^2y}{dx^2}\) + m²y = 0

Answer»

Given y = sinmx

\(\frac{dy}{dx}\) = -mcosmx

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

∴ \(\frac{d^2y}{dx^2}\) + m²y = 0

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