1. Consider the differential equation i+4x+3x=u with input u the output y = x. 1.a Write the system into first order form and calculate the A, B, C, D matrices. 1.b Calculate the eigenvalues and...

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Extracted text: 1. Consider the differential equation i+4x+3x=u with input u the output y = x. 1.a Write the system into first order form and calculate the A, B, C, D matrices. 1.b Calculate the eigenvalues and eigenvectors of the matrix A and calculate the matrix exponential eA. 1.c Using the results in part (b) derive the free response considering the initial conditions x(0) =1, ¿(0) = 2. 1.d Now consider the input u(t) = e' and calculate the forced part of the solution y(t) using the convolution integral and plot the full solution (free + forced). [To evaluate the integral you may use symbolic packages.]