1 . Given the differential equation * ( + ) + 4 * ( t ) = 3 x ( t ) ( a ) Find the characteristic polynomial , equation , roots , and modes of the system . ( b ) Find the zero - input response , Yo ( t ) , for t = O if the initial conditions are yo( 0 ) = 0 and jo( 0 ) = 2 ( C ) Find the unit impulse response of the system , A(t ) . ( d) Using the convolution table , find the system zero - state response to an input* ( + ) = e " "(t ) . ( @ ) Write the total response of the system . ( I )` What are the natural response and the forced response of the system