Question

[15] Use Laplace transform to solve the following differential equations (i.e.,solve for y(t)) \frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}-4 y=e^{-t} u(t) \text { with } y(0)=I \text { and }

\frac{d y(0)}{d t}=0 \frac{d^{2} y}{d t^{2}}+6 \frac{d y}{d t}+25 y=\frac{d x}{d t}+2 x \text { where } x(t)=25 u(t) \text { and ICs are } y(0)=1 \text { and } \frac{d y(0)}{d t}=1 \text { c. } D^{2} y(t)+D y(t)+2 y(t)=x(t) \text { where } x(t)=2 u(t) \text { and ICs are zero }

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