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