Continuous-Time System:
a1 = 14, a0 = 10, b1 = 8, b0 = 1, 

Your excitation signal x(t) consists of straight lines connecting these points.
It has been zero up until the first time and is zero after the last time.

t = 1.94427, x(t) = 0
t = 1.94427, x(t) = -4
t = 2.07686, x(t) = -4
t = 2.07686, x(t) = 8
t = 2.37155, x(t) = 8
t = 2.37155, x(t) = -4
t = 3.37294, x(t) = -4
t = 3.37294, x(t) = 9
t = 4.10884, x(t) = 9
t = 4.10884, x(t) = -10
t = 6.45239, x(t) = -10
t = 6.45239, x(t) = 0
t = 13.6895, x(t) = 0

Discrete-Time System:
a0 = 22, a1 = 19, b0 = 51, b1 = 10, 
0 <= n < 2,  x[n] = 0
2 <= n < 11,  x[n] = -13
11 <= n < 12,  x[n] = -17
12 <= n < 15,  x[n] = 8
15 <= n < 29,  x[n] = 0

x[n] has been zero up until the first time and is zero after the last time.