Final answer:
The given system is linear because it satisfies the principle of superposition and homogeneity.
Step-by-step explanation:
A system is considered linear if it satisfies the principle of superposition and homogeneity. The given system is linear because it satisfies both of these conditions. Let's break down the system:
The first term d²y/dt² is a derivative, and derivatives are linear operators, so it satisfies the principle of superposition.
The second term 3y is a multiplication by a constant, and scalar multiplication is also a linear operation, so it satisfies homogeneity.
The third term ∫(2x+cosx)dt is an integral and integrals are linear operators. The last term dx/dt is a derivative and derivatives are linear operators.
Therefore, with all terms being linear operators, the given system is linear.