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(1 point) Let 9 -4 15 -7' 6e3' +2e-t 9e3' +5e' y,(t) a. Show that yi(t)...
Consider the initial value problem s' (t) = Ayt), y(0) = 13): where A is a...
Consider the initial value problem s' (t) = Ayt), y(0) = 13): where A is a 2 x 2 matrix and y= Yi , 1. You are given that the eigenvalues and eigenvectors of A are Ly2 11 = -1, 41 = and 12 = -4, 92 = 0,21 The solution of the initial value problem is y1 = -5e-t+6e-4t y2 = 3e-t - 3e-4t yy = -5e-4t +6e-t y2 = 3e-4t - 3e-t = -3et+4e-4t = 2e-t – 2e-4t...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
(1 point) In this exercise you will solve the initial value problem e-9 y" – 184'...
(1 point) In this exercise you will solve the initial value problem e-9 y" – 184' +81y = 4472; y(0) = -3, v'(0) = -2. (1) Let C and Cybe arbitrary constants. The general solution to the related homogeneous differential equation y" – 18y' +81y = 0 is the function yh() = C1 yı() + C2 y2() = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(T) + C29(2) #C19() +C2f(). is of...
(1 point) In general for a non-homogeneous problem " ()y r)y-f(x) assume that yi, ye is...
(1 point) In general for a non-homogeneous problem " ()y r)y-f(x) assume that yi, ye is a fundamental set of solutions for the homogeneous problem y"+p(r)y' +(xy-0. Then the formula for the particular solution using the method of variation of parameters is are where W(z) is the Wronskian given by the determinant where ufe) and u ,-1-nent), d dz. NOTE When evaluating these indefinite integrals we take the arbitrary constant of integration to be zero. So we have- Wed and...
Let y(t) be the solution to y = t + y satisfying y(6) = 4. Use...
Let y(t) be the solution to y = t + y satisfying y(6) = 4. Use Euler's Method with time step h = 0.1 to approximate y(6.5). (Use decimal notation. Give your answers to four decimal places.) n= 0, to = 6, Yo = n = 1, 1 = 6.1, yı = n = 2,12 = 6.2, y2 = n= 3, 13 = 6.3, y3 = n= 4,14 = 6.4, y4 = n= 5,15 = 6.5, ys =
4. Let (Yi] be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal with period 4, that is, st-st+4, t-1, 2, . . . , and Xt = a + bt + ct2 + st + Y. (i) Let (ho,...
4. Let (Yi] be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal with period 4, that is, st-st+4, t-1, 2, . . . , and Xt = a + bt + ct2 + st + Y. (i) Let (ho, do )-min( (k, d)such that k > 0, d 0, and the proces s W t ▽k▽dX,-(1 B)a Find ko and do. For W, (with k = ko and d...
(4) Let Yi, . .. ,y, be Ņ(θ, 1). Let θ,-yn and θ2-7. (a) What are...
(4) Let Yi, . .. ,y, be Ņ(θ, 1). Let θ,-yn and θ2-7. (a) What are the possible values of the θ (b) Find the bias and MSE of both the estimators. (c) Is one of the estimators better than the other? (d) For what values of θ is better than θ2?
(1 point) Consider the linear system 3 2 ' = y. -5 -3 a. Find the...
(1 point) Consider the linear system 3 2 ' = y. -5 -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 = 15 and 2 V2 b. Find the real-valued solution to the initial value problem Syi ly 3y1 + 2y2, -541 – 3y2, yı(0) = 0, y2(0) = -5. Use t as the independent variable in your answers. yı(t) y2(t)
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y}...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
(1 point) Consider the linear system 3 y y 5 3 a. Find the eigenvalues and...
(1 point) Consider the linear system 3 y y 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 0 and A2 = -1 02 -3- -3+1 b. Find the real-valued solution to the initial value problem Svi C = -3y - 2y2, 591 +372 y.(0) = 6, 32(0) = -15. Use t as the independent variable in your answers. yı() y2(t) = 0
Consider the initial value problem s' (t) = Ayt), y(0) = 13): where A is a 2 x 2 matrix and y= Yi , 1. You are given that the eigenvalues and eigenvectors of A are Ly2 11 = -1, 41 = and 12 = -4, 92 = 0,21 The solution of the initial value problem is y1 = -5e-t+6e-4t y2 = 3e-t - 3e-4t yy = -5e-4t +6e-t y2 = 3e-4t - 3e-t = -3et+4e-4t = 2e-t – 2e-4t...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
(1 point) In this exercise you will solve the initial value problem e-9 y" – 184' +81y = 4472; y(0) = -3, v'(0) = -2. (1) Let C and Cybe arbitrary constants. The general solution to the related homogeneous differential equation y" – 18y' +81y = 0 is the function yh() = C1 yı() + C2 y2() = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(T) + C29(2) #C19() +C2f(). is of...
(1 point) In general for a non-homogeneous problem " ()y r)y-f(x) assume that yi, ye is a fundamental set of solutions for the homogeneous problem y"+p(r)y' +(xy-0. Then the formula for the particular solution using the method of variation of parameters is are where W(z) is the Wronskian given by the determinant where ufe) and u ,-1-nent), d dz. NOTE When evaluating these indefinite integrals we take the arbitrary constant of integration to be zero. So we have- Wed and...
Let y(t) be the solution to y = t + y satisfying y(6) = 4. Use Euler's Method with time step h = 0.1 to approximate y(6.5). (Use decimal notation. Give your answers to four decimal places.) n= 0, to = 6, Yo = n = 1, 1 = 6.1, yı = n = 2,12 = 6.2, y2 = n= 3, 13 = 6.3, y3 = n= 4,14 = 6.4, y4 = n= 5,15 = 6.5, ys =
4. Let (Yi] be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal with period 4, that is, st-st+4, t-1, 2, . . . , and Xt = a + bt + ct2 + st + Y. (i) Let (ho, do )-min( (k, d)such that k > 0, d 0, and the proces s W t ▽k▽dX,-(1 B)a Find ko and do. For W, (with k = ko and d...
(4) Let Yi, . .. ,y, be Ņ(θ, 1). Let θ,-yn and θ2-7. (a) What are the possible values of the θ (b) Find the bias and MSE of both the estimators. (c) Is one of the estimators better than the other? (d) For what values of θ is better than θ2?
(1 point) Consider the linear system 3 2 ' = y. -5 -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 = 15 and 2 V2 b. Find the real-valued solution to the initial value problem Syi ly 3y1 + 2y2, -541 – 3y2, yı(0) = 0, y2(0) = -5. Use t as the independent variable in your answers. yı(t) y2(t)
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
(1 point) Consider the linear system 3 y y 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 0 and A2 = -1 02 -3- -3+1 b. Find the real-valued solution to the initial value problem Svi C = -3y - 2y2, 591 +372 y.(0) = 6, 32(0) = -15. Use t as the independent variable in your answers. yı() y2(t) = 0
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