A system is represented dy/dt + 2y = 4tu(t). The ramp constant

A system is represented ^dy/_dt + 2y = 4tu(t). The ramp constant in the forced response will be

dy/dt + 2y = 4 t u (t)
Laplace transform is, 5y(s) + 2y(s) = 4/s²
or y(s) [s + 2] = 4/s²
or y (s)= 4/s² [s + 2]

∴ y(s) = -	1	+	2	+	1
	s		s²		s + 2

= – u (t) + 2 tu (t) + e^{– 2t}
forced response terms.