Convert the second-order initial-value problem into a system of first-order initial value problems. y'' + 7y'...
Convert the second-order initial-value problem into a system of first-order initial value problems.
y'' + 7y' + 2y = e^(3x)
y'(0)=1
y''(0)=1
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Convert the second-order initial-value problem into a system of
first-order initial value problems.
y'' + 7y'...
Problem #8: Solve the following initial value problem. y'" – 7y" - 5y' + 75y =...
Problem #8: Solve the following initial value problem. y'" – 7y" - 5y' + 75y = 0, y(0) = 0, y'0) = 0, y"(0) = 8 -1/2*e^(-3*x) + 1/2*e^(5*x) Enter your answer as a symbolic function of x, as in these examples Problem #8: Do not include 'y = 'in your answer. -1e-3x + žex Just Save Your work has been saved! (Back to Admin Page) Submit Problem #8 for Grading Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem...
(1 point) Use the Laplace transform to solve the following initial value problem: y"-7y+10y 0, (0)...
(1 point) Use the Laplace transform to solve the following initial value problem: y"-7y+10y 0, (0) 6, /(0) -3 (1) First, using Y for the Laplace transform of y(t), Le, Y find the equation you get by taking the Laplace transform of the differential equation to obtain C() 0 (2) Next solve for Y A (3) Now write the above answer in its partial fraction form, Y + 8-6 8a (NOTE: the order that you enter your answers matter so...
Problem 1. Find the solution to the following initial value problems. (a) y'" – y" –...
Problem 1. Find the solution to the following initial value problems. (a) y'" – y" – 4y' + 4y = 0; y(0) = -4, y'(0) = -1, y"(0) = -19. (b) y'' – 4y"' + 7y – by = 0; y(0) = 1, y'(0) = 0, y"(O) = 0.
Cosider the second order initial value problem y = y'exp(-3 y) - 2+y+12, 1€ [2,4), y(2)...
Cosider the second order initial value problem y = y'exp(-3 y) - 2+y+12, 1€ [2,4), y(2) = 3, y' (2) = 1. (a) (1 mark] To convert this into a system of first order ODEs, we introduce *1 = y and *2 = y.Then we obtain the first order system * = 50.0) = (4920:09 where | 12(1,x) fit,x) = x2 f2(t, x) = (Hint: Your expressions should be in terms of t, x] and x2 and should not contain...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x + 7y > 21 --x+y> -5 x,y > 0 2. Maximize Z= 2x + 2y subject to 2x - y > -4 x - 2y < 4 x+y = 6 Xy0
1. (Exercise*) Solve the first order initial value problem y + 2y =t(ui(t) – uz(t)) subject...
1. (Exercise*) Solve the first order initial value problem y + 2y =t(ui(t) – uz(t)) subject to y(0) = 0.
5.3.1 Convert the given initial value problem into an initial value problem for a system in...
5.3.1 Convert the given initial value problem into an initial value problem for a system in normal form. y"(t) - 4y'(t) + 58+ y(t) = 7t y(0) = 3, y'(0) = - 3 Let xy = y and X2 = y'. Complete the differential equation and initial condition for X (Type an expression using t, xy, and X2 as the variables.) x'= X (0)=
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the syste...
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the system in the matrix form: 3) Find the eigenvalues: 4) Find associated eigenvector(s): 5) Write the general solution of the system figure out the c and c2 To find the particular soluion 6) 2 7) Find the particular solution of the system 8) Write the particular solution of...
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answ...
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answer in terms of w,y, z. Problem 4 Solve the above problem by applying Laplace transform to the whole system without transferring it to a single equation. Do you get the same answer as in problem1? (Hint: Denote W(s), Y (s), Z(s) to be Laplace transforms of w(t),...
Find the solution of the following nonhomogeneous 2nd order linear initial value problem: | 1. y”...
Find the solution of the following nonhomogeneous 2nd order linear initial value problem: | 1. y” + 7y + 10y = 176e6t, y (0) = 0, y'(0) = 13 2. y” + 7y + 10y = 140 cos(4t) – 30 sin(4t) y(0) = 1, y'(0) = 0
Problem #8: Solve the following initial value problem. y'" – 7y" - 5y' + 75y = 0, y(0) = 0, y'0) = 0, y"(0) = 8 -1/2*e^(-3*x) + 1/2*e^(5*x) Enter your answer as a symbolic function of x, as in these examples Problem #8: Do not include 'y = 'in your answer. -1e-3x + žex Just Save Your work has been saved! (Back to Admin Page) Submit Problem #8 for Grading Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem...
(1 point) Use the Laplace transform to solve the following initial value problem: y"-7y+10y 0, (0) 6, /(0) -3 (1) First, using Y for the Laplace transform of y(t), Le, Y find the equation you get by taking the Laplace transform of the differential equation to obtain C() 0 (2) Next solve for Y A (3) Now write the above answer in its partial fraction form, Y + 8-6 8a (NOTE: the order that you enter your answers matter so...
Problem 1. Find the solution to the following initial value problems. (a) y'" – y" – 4y' + 4y = 0; y(0) = -4, y'(0) = -1, y"(0) = -19. (b) y'' – 4y"' + 7y – by = 0; y(0) = 1, y'(0) = 0, y"(O) = 0.
Cosider the second order initial value problem y = y'exp(-3 y) - 2+y+12, 1€ [2,4), y(2) = 3, y' (2) = 1. (a) (1 mark] To convert this into a system of first order ODEs, we introduce *1 = y and *2 = y.Then we obtain the first order system * = 50.0) = (4920:09 where | 12(1,x) fit,x) = x2 f2(t, x) = (Hint: Your expressions should be in terms of t, x] and x2 and should not contain...
PROBLEMS 7.3 1. Minimize Z= 6x + 14y subject to 14x + 7y > 43 3x + 7y > 21 --x+y> -5 x,y > 0 2. Maximize Z= 2x + 2y subject to 2x - y > -4 x - 2y < 4 x+y = 6 Xy0
1. (Exercise*) Solve the first order initial value problem y + 2y =t(ui(t) – uz(t)) subject to y(0) = 0.
5.3.1 Convert the given initial value problem into an initial value problem for a system in normal form. y"(t) - 4y'(t) + 58+ y(t) = 7t y(0) = 3, y'(0) = - 3 Let xy = y and X2 = y'. Complete the differential equation and initial condition for X (Type an expression using t, xy, and X2 as the variables.) x'= X (0)=
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the system in the matrix form: 3) Find the eigenvalues: 4) Find associated eigenvector(s): 5) Write the general solution of the system figure out the c and c2 To find the particular soluion 6) 2 7) Find the particular solution of the system 8) Write the particular solution of...
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answer in terms of w,y, z. Problem 4 Solve the above problem by applying Laplace transform to the whole system without transferring it to a single equation. Do you get the same answer as in problem1? (Hint: Denote W(s), Y (s), Z(s) to be Laplace transforms of w(t),...
Find the solution of the following nonhomogeneous 2nd order linear initial value problem: | 1. y” + 7y + 10y = 176e6t, y (0) = 0, y'(0) = 13 2. y” + 7y + 10y = 140 cos(4t) – 30 sin(4t) y(0) = 1, y'(0) = 0
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