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(Solved): 3. (a) Compute the general solution for: \( \frac{d^{2} y}{d t^{2}}+4 \frac{d y}{d t}+3 y=e^{-t / 2 ...
3. (a) Compute the general solution for: \( \frac{d^{2} y}{d t^{2}}+4 \frac{d y}{d t}+3 y=e^{-t / 2} \). (b) Compute the solution with \( y(0)=y^{\prime}(0)=0 \). (c) Describe the long-term behavior of solution in a brief paragraph.