Write the correct alternative in the following:

Question:

Write the correct alternative in the following:

If $y=a \sin m x+b \cos m x$, then $\frac{d^{2} y}{d x^{2}}$ is equal to

A. $-m^{2} y$

B. $m^{2} y$

C. $-\mathrm{my}$

D. $m y$

Solution:

Given:

$y=a \sin m x+b \cos m x$

$\frac{d y}{d x}=m a \cos m x-m b \sin m x$

$\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=-\mathrm{m}^{2} \mathrm{a} \sin \mathrm{m} \mathrm{x}-\mathrm{m}^{2} \mathrm{~b} \cos \mathrm{m} \mathrm{x}$

$=-m^{2}[a \sin m x+b \cos m x]$

$=-m^{2} y$

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