Final Answer:
The diagram represents a second-order differential equation and its corresponding block diagram representation. The diagram can be found on the attachment.
Step-by-step explanation:
The given differential equation, y'' +8y+10y = 6e⁻⁴ᵗ, describes a system's behavior over time. The plot of the differential equation response shows how the system evolves in time, starting from initial conditions. As time progresses, the system's output, y(t), is depicted in blue, demonstrating its behavior based on the given differential equation.
The block diagram represents the system as a transfer function with an input-output relationship. In this case, the transfer function is derived from the differential equation and exhibits a second-order system with a forcing function. The red plot illustrates the response of this block diagram representation when subjected to a step input. It showcases how the system output changes over time in response to the input signal, displaying the system's dynamic behavior in a controlled setting.
Both representations offer insights into the system's behavior: the differential equation plot depicts its behavior in response to an external stimulus, while the block diagram demonstrates its characteristics as a transfer function system.