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

Answer 1

(a) −m²y

Here,

\[y = a \sin mx + b \cos mx\]

\[ \Rightarrow \frac{d y}{d x} = am \cos mx - bm \sin mx\]

\[ \Rightarrow \frac{d^2 y}{d x^2} = - a m^2 \sin mx - b m^2 \cos mx \]

\[ = - m^2 \left( a \sin mx + b \cos mx \right)\]

\[ = - m^2 y\]