The relationship between the input x(t) and output y(t)of

The relationship between the input x(t) and output y(t)of a causal system is defined as
d²y(t) - dy(t) - 2y(t) = 4x(t) + 5 dx(t)
dt² dt dt

The impulse response of system is

1. 3e^{– t} u(t) + 2e^2t u(– t)
2. (3e^{– t} + 2e^2t) u(t)
3. 3e^{– t} u(t) – 2e^2t u(– t)
4. (3e^{– t} – 2e^2t) u(– t)

Y(s) (s² – s – 2) = X (s) (5s – 4)

H(s) =	Y(s)	=	5s - 4
	X(s)		s ² - s - 2

=	3	+	2
	s + 1		s - 2

h(t) = 3e^{– t} u(t) + 2e^2t u(t).

d²y(t)	-	dy(t)	- 2y(t) = 4x(t) + 5	dx(t)
dt²	-	dt	- 2y(t) = 4x(t) + 5	dt