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Question
If y = a sin mx + b cos mx, then \[\frac{d^2 y}{d x^2}\] is equal to
Options
−m2y
m2y
−my
my
Solution
(a) −m2y
Here,
\[y = a \sin mx + b \cos mx\]
\[ \Rightarrow \frac{d y}{d x} = am \cos mx - bm \sin mx\]
\[ \Rightarrow \frac{d^2 y}{d x^2} = - a m^2 \sin mx - b m^2 \cos mx \]
\[ = - m^2 \left( a \sin mx + b \cos mx \right)\]
\[ = - m^2 y\]
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