I think there is an error in typing in the question. It should be
This is the equation of motion of S H M or simple harmonic motion. It is applicable for oscillations of a mass m attached at the end of a spring whose other end is tied to a wall or a rigid body. The same equation is applicable in a circular motion also.
Let y = A sin (ωx +Ф)
y' = d y/ d x = Aω cos (ωt + Ф)
y" = d² y / d x² = - A ω² sin (ω t + Ф ) = - A ω² y
So A = 1 and the solution is y = Sin (ω t + Ф)