2. find the time domain solution x(t) for the following differential equations (well, the second one is technically an integro-differential equation) using Laplace transforms. you will need to employ the

partial fraction expansion technique. \frac{d^{2} x}{d t^{2}}+6 \frac{d x}{d t}+25 x=e^{-t} x(0)=0 \left.\frac{d x}{d t}\right|_{t=0}=0 \frac{d^{2} x}{d t^{2}}+4 \frac{d x}{d t}+3 x=2 \int_{0}^{t} e^{-\tau} d \tau \left.\frac{d x}{d t}\right|_{t=0}=x(0)=0 (c) which solutions exhibit oscillatory behavior? link this to the poles of X(s). (d) which solutions exhibit convergent behavior? link this to the poles of X(s).