HW3 Q1: Find y(t), the zero-input component of the response for an LTIC system described by the following differential equations 1. (D+3D+2)y(t)=0, when the initial conditions are y(0) = 0 and y(0)=-5. 2. (D²+6D+9)y(t)=0, when the initial conditions are y(0)=3 and y(0)=-7. 3. (D2+4D+40)y(t)=(D+2)x(t), when the initial conditions are y(0)=2 and y(0)=16.78 Q2: Find the impulse response h(t) for systems specified by 1. (D+y(t)=x(1) 2. (D²+6D+9)y(t)=(D+2)x(t) Q3: Find the total solution of the following systems. Assume zero initial conditions. 1. (D-2)y(t)=sin(t) 2. (D2+2D+1)y(t)=eu(t)