How to Calculate ZIR for a Given Differential Equation?

[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.