Question

If y= sin mx prove that y"±m^2 y =0

Answer 1

Step-by-step explanation:

We have,

$y = \sin(mx)$

$\implies \: y ^{ \prime} = m \cos(mx)$

$\implies \: y ^{ \prime \prime} = m.m \{ - \sin(mx) \}$

$\implies \: y ^{ \prime \prime} = - m^{2} \sin(mx)$

$\implies \: y ^{ \prime \prime} = - m^{2} y$

$\implies \: y ^{ \prime \prime} + m^{2} y = 0$