The following question simply displays the importance of the principle of superposition in linear systems. Assuming zero initial conditions, the solutions below solve the given differential equation for two different inputs: - Differential Equation: dt2d2x+2dtdx+1x=f(t) - Solution 1: x1(t)=2et(et(t2)+t+2) for f(t)=f1(t)=2t - Solution 2: x2(t)=31et(3t+e3t1) for f(t)=f2(t)=3e2t Use the principle of superposition, to find the solution when f(t)=8t+9e2t