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Given y = acos(bx + c) .................1
=> dy/dx = -absin(bx + c)
d2 y/dx2 = -a(b2 )cos(bx + c) ........2
using equation 1 in equation 2, we get: d2 y/dx2 = -b2 y
=> d2 y/dx2 + b2 y = 0
This is the required differential eqaution.