The differential equation representing the family of curves $y=a \sin (\lambda x+\alpha)$ is :

• Correct answer
  A

  $\frac{d^2 y}{d x^2}+\lambda^2 y=0$
• B

  $\frac{d^2 y}{d x^2}-\lambda^2 y=0$
• C

  $\frac{d^2 y}{d x^2}+\lambda y=0$
• D

  None of the above

Hence, the correct answer is option: 'A'.