Verify that the piecewise-defined function y(x) =(−x2 x < 0 x2 x ≥0 is a solution of the differential equation xy0−2y = 0 where x ∈ (−∞,∞). Question 2 Consider the first order ODE: dy dx = (y−1)2 + ε1 where y(0) = 1 + ε2 for constants ε1 and ε2. Find the general solution to this problem, then plot the solution over the domain x ∈ [0,1] for ε1 = ε2 = 0, ε1 = 0 and ε2 = 0.01,...

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Find the Laplace Transforms of the following signals: a. δ(k1t+k2)       (k1 and k2 are constants)  b. ∑ 𝛅(𝐭 − 𝐤𝑻𝒐) ∞ 𝒌=𝟎  (To constant) 2. Show that the overall transfer function H(s) of the feedback system as shown in the figure below is ...

Description of procedure, indicating measurements taken Observations made during investigation, making note of any problems encountered which may have affected the results.  Results and Calculations  Tabulate all results/measurements taken during lab study. Tabulate all calculated results Show sample calculations for each type calculated result.  Discussion of results  Discuss all your results, making sure you address each objective in the light of your results. Discuss any d...

Energy Efficiency Residential Retrofit Plan (30%)- At the level of the individual or family, our house is a major source of greenhouse gas emissions and consumption decisions. All buildings are expected to be net zero energy by 2030, so move your family to this sustainability goal early with a retrofit to achieve net zero energy on an annual basis, (or, if you want to be more ambitious, net zero carbon by offsetting embedded greenhouse gases as well). 1. Choose a location for your house and prep...

 Implement Matching Pursuit (MP) and Orthogonal Matching Pursuit (OMP) algorithms. b. Compute the coherence of D : µ = maxd,d0∈D|hd,d0i| c. Write a procedure that generates a vector x = Da by picking K random positions in a and sets those positions to random numbers (normal distribution). Then write a procedure that reports the error in recovering a from x by using the MP and OMP algorithms. d. Vary the level of sparsity in a (subset) of the range 1 ≤ K ≤ d. For each sparsi...

Prove that for every set X containing four integers there is a non-empty subset of X, the sum of whose elements is exactly divisible by 4....