Classify the following PDE as (i) Linear or Nonlinear, (ii) Homogeneous ornonhomogeneous a. (y + 2)2u24– 2x log ya²u+ k- In u 3 2е-*, k > 0диax?ду?дуb. и хх + хуиху + у?и? %3D0a?u= v2 +x-azuC. t-at2x+Z^ =

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Answered: а. (у + 2)2— 2x log y - In u = 2e-x, k…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A linear multiple regression model is given as: Y = βo + β1 X1 + β2 X2 + μ a. Determine the parameters of this model b. Explain the circumstance under which X1 be called an endogenous variable?
2. We would like to fit a linear regression estimate to the dataset {(x®,y@),(x), y),., (x(N), g/N)} with x e RM by minimizing the ordinary least square (OLS) objective function: N M -Συ, .(i) J(w): j=1 Specifically, we solve for each coefficient wk (1< k < M) by deriving an expression of Wk from the critical point J(w) the dataset (x(1), y(1)), (x(2), y(2)), . 0. What is the expression for each wk in terms of … , (x(^), y(N) and w1, , wk-1, Wk+1; *** , WM? .. .. Select one: E, (y() –D,-1,j+k W;x;") i=D1 Wk = =1 O Wk
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7. a) What are residual plots and box plots? b) Do the stability analysis of the following model which is formulated to study the effect of toxicant on one competing species where the environmental toxicant concentration is being taken to change w.r.t. time. dN = rN, - α,Ν,N, - d,C,N , dt dN2 = rN, - α,N,., dt dCo = k,P - g,C, – m¡C, dt dP Q- hp – kPN, + gC,N . dt along with the initial conditions. N, (0) = N10,N2 (0)= N20,C, (0)= 0, P(0)= P, > 0 %3D Here, N1 (t) = Density of prey population
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I estimate a multiple linear regression model for portfolio using market size and value and adding as usual a constant ( to make sure that E(errors)=0 as per the GM assumptions request ). Then I wish to identify monthly effects so I generate a dummy for each month of the year , from January to December included . EViews will Select one: a. send out an error message saying : near singular matrix . This is happening because I fell into the dummy variable trap because the sum of all the dummy variables is at any point in time equal to 1 . As a consequence the OLS estimator is not identified b. send out an error message saying : near singular matrix . This is happening because I fell into the dummy variable trap because the costant (c) multiplies the regressor 1 and the sum of all the dummy variable is at any point in time equal to 1 . As a consequence the model is not identified and no estimator can estimate the betas c. send out an error message saying : near singular…
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а. (у + 2)2— 2x log y - In u = 2e-x, k > 0 ay ax? ду? b. uxx + xy uxy + y²u² = 0 = v2 + x azu C. t- a²u X- at2 %3D