The differenital equation representing the family of curves
` y =a sin (lambdax +alpha) ` is :

Options

A. ` (d^(2)y)/(dx^(2))+ lambda^(2)y =0`
B. ` (d^(2)y)/(dx^(2)) - lambda^(2) y=0`
C. ` (d^(2)y)/(dx^(2)) + lambda y=0`
D. none of the above

Answer

B

Explanation

Let y = ` a sin ( lambda x +alpha)`
` Rightarrow (dy)/(dx) = lambda a cos ( lambda x +alpha)`
Again differentiating on both side we get
` (d^(2)y)/(dx^(2)) = -lambda a sin (x + alpha)`
` Rightarrow (d^(2)y)/(dx^(2)) + lambda^(2) y=0` Required equation.