Other examples of linear systems include those described by y ( t ) = k x ( t ) , y ( t ) = k d x ( t ) d t , y ( t ) = k ∫ ∫ − − ∞ ∞ t x ( τ τ ) d τ τ , and any system described by ordinary linear differential equations. Systems described by y ( t ) = k , y ( t ) = k x ( t ) + k 0 , y ( t ) = sin ⁡ ⁡ [ x ( t ) ] , y ( t ) = cos ⁡ ⁡ [ x ( t ) ] , y ( t ) = x 2 ( t ) , y ( t ) = x ( t ) , y ( t ) = | x ( t ) | , and a system with odd-symmetry output consisting of a linear region and a saturation (constant) region, are non-linear because they don't always satisfy the superposition principle.