(Solution Library) Rewrite the n -th order linear differential equation y^(n)(t)+a_n-1(t) y^(n-1)(t)+•s+a_0(t) y(t)=b_0(t) u(t)+b_1(t) u^(1)(t) as
Question: Rewrite the \(\mathrm{n}\) -th order linear differential equation
\[y^{(n)}(t)+a_{n-1}(t) y^{(n-1)}(t)+\cdots+a_{0}(t) y(t)=b_{0}(t) u(t)+b_{1}(t) u^{(1)}(t)\]as a dimensional- \(n\) linear equation in standard state-space form:
\[\left\{ \begin{array}{*{35}{l}} x'(t)=A(t)x(t)+B(t)u(t) \\ y'(t)=C(t)x(t)+D(t)u(t) \\ \end{array} \right.\]Note that \(y^{(k)}(t)\) denotes the \(\mathrm{k}\) -th order time derivative of \(y(t)\)
Deliverable: Word Document 
![[Solved] Compute \Phi(t, 0) for A(t)=(llt t](/images/solutions/MC-solution-library-72189.jpg "[Solved] Compute \Phi(t, 0) for A(t)=(llt t , 0")
[Solved] Compute \Phi(t, 0) for A(t)=(llt t , 0
(Steps Shown) Suppose A(t) is T-periodic. Prove that for every
(All Steps) X and Y are i.i.d. random variables with common p.d.f.
Solution: Prove that adding 12 i.i.d. RVs each on U(0,1) yields
![[Solution Library] Take two Gaussian RVs X](/images/solutions/MC-solution-library-72193.jpg "[Solution Library] Take two Gaussian RVs X and Y generated from part")
[Solution Library] Take two Gaussian RVs X and Y generated from part
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