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In this problem, we will investigate the strategy to deal with repeated eigenvalues in two wavs. Consider A-I 7-2-6...
we assume that X solves the differential equation X'=AX. In this problem, we will investigate the strategy to deal...
we assume that X solves the differential equation X'=AX.
In this problem, we will investigate the strategy to deal with repeated eigenvalues. Conside:r A=17-2-6 1. This matrix has only one eigenvalue Ao of multiplicity 3. Find the characteristic equation, the eigenvalue λ0 and an eigenvector P for λ0 2. Find vectors K. L such that (A-X0IK-P and (A-X01)L-K. Compute the matrix M-1AM where M-(PIKL) 3. Let Y -M'X. Solve the equation for Y in the following manner : first, solve...
please solve all 3 Differential Equation problems 3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)...
please solve all 3 Differential Equation problems
3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)-0 (a) Show that λ =0 is not an eigenvalue (b) Show that the eigenfunctions are the functions {sin α11,o, where αη įs the nth positive root of the equation tan z -z (c) Draw a sketch indicating the roots as the points of intersection of the curves y tan z and y...
2. (3+4+4+4 pts) In this problem, we discuss a method of solving SOL equations known as...
2. (3+4+4+4 pts) In this problem, we discuss a method of solving SOL equations known as Reduction of Order. Given an equation y" +p(a)y' +9(2)y = 0, and assuming yi is a solution, Reduction of Order asks: does there exist a second, linearly-independent solution y2 of the form y2 = u(x)41 for some function u(x)? See Section 3.2, Exercise 36 for reference). We'll now use this to solve the following problem. (a) Consider the SOL differential equation sin(x)y" — 2...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0,...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy =...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy = 0 (1) where a, b, c are constants satisfy so that y(x) = x (a) Find and justify what conditions should a constant m to (1) is a solution (b) Using your solution to (1) Write these three different cases as an equation that a, b,c satisfy. Hint: Use the quadratic formula we should get three different cases for the values that m can...
Question 8 please 5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write...
Question 8 please
5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write the time derivative as 2.4(x, t) = V(x,+) - (xt), where At is a sufficiently small increment of time. Plug the algebraic form of the derivative into Schrodinger's Eq. and solve for '(x,t+At). b. Put your answer in the form (x,t+At) = T '(x,t). c. What physically does the operator T do to the function '(x,t)? d. Deduce an expression for '(x,t+24t), in terms...
Elementary Differential Equation Unit Step Function Problem Project 2 A Spring-Mass Event Problenm A mass of...
Elementary Differential Equation Unit Step Function Problem
Project 2 A Spring-Mass Event Problenm A mass of magnitude m is confined to one-dimensional motion between two springs on a frictionless horizontal surface, as shown in Figure 4.P.3. The mass, which is unattached to either spring, undergoes simple inertial motion whenever the distance from the origin of the center point of the mass, x, satisfies lxl < L. When x 2 L, the mass is in contact with the spring on the...
we assume that X solves the differential equation X'=AX.
In this problem, we will investigate the strategy to deal with repeated eigenvalues. Conside:r A=17-2-6 1. This matrix has only one eigenvalue Ao of multiplicity 3. Find the characteristic equation, the eigenvalue λ0 and an eigenvector P for λ0 2. Find vectors K. L such that (A-X0IK-P and (A-X01)L-K. Compute the matrix M-1AM where M-(PIKL) 3. Let Y -M'X. Solve the equation for Y in the following manner : first, solve...
please solve all 3 Differential Equation problems
3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)-0 (a) Show that λ =0 is not an eigenvalue (b) Show that the eigenfunctions are the functions {sin α11,o, where αη įs the nth positive root of the equation tan z -z (c) Draw a sketch indicating the roots as the points of intersection of the curves y tan z and y...
2. (3+4+4+4 pts) In this problem, we discuss a method of solving SOL equations known as Reduction of Order. Given an equation y" +p(a)y' +9(2)y = 0, and assuming yi is a solution, Reduction of Order asks: does there exist a second, linearly-independent solution y2 of the form y2 = u(x)41 for some function u(x)? See Section 3.2, Exercise 36 for reference). We'll now use this to solve the following problem. (a) Consider the SOL differential equation sin(x)y" — 2...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy = 0 (1) where a, b, c are constants satisfy so that y(x) = x (a) Find and justify what conditions should a constant m to (1) is a solution (b) Using your solution to (1) Write these three different cases as an equation that a, b,c satisfy. Hint: Use the quadratic formula we should get three different cases for the values that m can...
Question 8 please
5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write the time derivative as 2.4(x, t) = V(x,+) - (xt), where At is a sufficiently small increment of time. Plug the algebraic form of the derivative into Schrodinger's Eq. and solve for '(x,t+At). b. Put your answer in the form (x,t+At) = T '(x,t). c. What physically does the operator T do to the function '(x,t)? d. Deduce an expression for '(x,t+24t), in terms...
Elementary Differential Equation Unit Step Function Problem
Project 2 A Spring-Mass Event Problenm A mass of magnitude m is confined to one-dimensional motion between two springs on a frictionless horizontal surface, as shown in Figure 4.P.3. The mass, which is unattached to either spring, undergoes simple inertial motion whenever the distance from the origin of the center point of the mass, x, satisfies lxl < L. When x 2 L, the mass is in contact with the spring on the...
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