Finding ZIR given a diff eq

[MooseBoys]

Homework Statement

Calculate ZIR(t) for the system described for the following differential equation, where the initial condition is y(0-) = 5:

Homework Equations

2y' + 3y = 2x' + x(t-1)

The Attempt at a Solution

I'm pretty sure we're supposed to laplace-transform it, then find Y/X = H(s) then inverse back to time domain.
2*(s*Y - 5) + 4*Y = 2*(s*X) + X*exp(-s)
cannot be solved for Y/X, which makes me think I somehow messeed up the initial transform, or perhaps the method altogether

 

[SGT]

Homework Statement

Calculate ZIR(t) for the system described for the following differential equation, where the initial condition is y(0-) = 5:

Homework Equations

2y' + 3y = 2x' + x(t-1)

The Attempt at a Solution

I'm pretty sure we're supposed to laplace-transform it, then find Y/X = H(s) then inverse back to time domain.
2*(s*Y - 5) + 4*Y = 2*(s*X) + X*exp(-s)
cannot be solved for Y/X, which makes me think I somehow messeed up the initial transform, or perhaps the method altogether

For the ZIR you must have no imput. So, you must solve
2y´ + 3 y = 0 with y(0) = 5
For the zero state response you solve
2y´ + 3y = 2x´+ x(t-1)
The complete response is the sum of the two.

 

[piercas]

I would first commend the student for their attempt at solving the problem using Laplace transforms. This is a valid approach and shows a good understanding of the concept. However, I would suggest checking the initial conditions and making sure the Laplace transform was done correctly. It is also important to double check the algebra when solving for Y/X. If the problem persists, I would recommend seeking assistance from a teacher or classmate to ensure accuracy in the solution. Additionally, it may be helpful to review the Laplace transform method and practice more problems to gain a better understanding of the concept.