1. The problem statement, all variables and given/known data Find the zero input and zero state response for the following system y''(t) + 3y'(t) + 2y(t) = 2 x'(t) - x(t-1) where x(t) = (2e^-t)*u(t) U(t) is the step function 2. Relevant equations Y = Yh + Yp Y = Yzsr + Yzir 3. The attempt at a solution I can't find any similar examples online and im partially thrown off by the u(t) step function, and it's derivative the ζ(t) function. I have no issues finding the homogenous equation, but the particular part is confusing, specifically finding coefficients. There are no table forms I can find that I can plug back into the differential equation to solve for. To start finding the particular form, I used the product rule with the step function right hand side of equation = (-4*e^-t)*u(t) + (4*e^-t)*ζ(t) - 2*e^-(t-1)*u(t) But I have no idea how to solve for coefficients of this system, basically stuck and I am not able to find the zero state response without finding the particular form.