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3. Consider the boundary value problem (a) Using the Rayleigh quotient, show that λ (b) Show that...
Consider the following boundary value problem, x2y′′ + 17xy′ + (64 + λ) y = 0, y(1) ...
Consider the following boundary value problem,
x2y′′ + 17xy′ + (64 +
λ) y = 0, y(1)
= 0, y(e6 ) = 0
(a)
Find the eigenvalues.
(b)
Find the eigenfunctions. Take the arbitrary constant (either
c1 or c2) from the general
solution to be 1.
Consider the following boundary value problem, xy" + 17xy' + (64 + 2) y = 0, y(1) = 0, yle) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either...
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determi...
#2 ONLY PLEASE
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouville form: do Given a(z), 3(2), and 7(2), what are p(x), σ(x), and q(x) 2. Consider the eigenvalue problem (a) Use the result from the previous problem to put this in Sturm-Liouville form (b) Using the Rayleigh quotient, show that λ > 0. (c) Solve this equation subject to the boundary conditions and determine...
3. (10 Points, part III) Consider the Sturm-Liouville differential equation where the coefficients p(z), q(z), and...
3. (10 Points, part III) Consider the Sturm-Liouville differential equation where the coefficients p(z), q(z), and σ(z) are real and continous on la, b , and p(2) and σ(z) are strictly positive for all a,b (a) Derive the Rayleigh quotient λ from (2). b) What does this quotient describe? Give two examples of applications for this formula. (c) what are the neces,ary conditions for λ > 0 to be satisfied? (d) Recall that the minimum value of the Rayleigh quotient...
Consider these two boundary-value problems: Show that if x is a solution of boundary-value problem,... clear steps and brief explanation please 7. Consider these two boundary-value problems: . x-f (t...
Consider these two boundary-value problems: Show that if x is a
solution of boundary-value problem,...
clear steps and brief explanation please
7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution of boundary-value problem ii, then the function y(t) - x((t- a)/h) solves boundary-value problem i, where h b- a.
7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution...
4. Consider the following initial value problem of the 1D wave equation with mixed boundary condition...
4. Consider the following initial value problem of the 1D wave equation with mixed boundary condition IC: u(z, t = 0) = g(x), ut(z, t = 0) = h(z), BC: u(0, t)0, u(l,t) 0, t>0 0 < x < 1, (a)Use the energy method to show that there is at most one solution for the initial-boundary value problem. (b)Suppose u(x,t)-X()T(t) is a seperable solution. Show that X and T satisfy for some λ E R. Find all the eigenvalues An...
3. Consider the eigenvalue problem 1
The answer is given. Please show more detailed steps, thank
you.
3. Consider the eigenvalue problem 1<x<2 dx2 y(1)=0,y(2) = 0. dx iwrite it in the standard Sturm-Liouville form. ii) Show that 0 by the Rayleigh Quotient. dx p(x)-x, q(x) = 0, σ(x)-1 According the Raileigh Quotient Any eigenvalue is related to its eigenfunction φ(x) by - x p(x) dr Since the B.C. are ф(1)-0 and ф(2-0, so dx
3. Consider the eigenvalue problem 1
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value probl...
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
3. Consider the boundary value problem for y(x), -1 < x < 1: **) g” +...
3. Consider the boundary value problem for y(x), -1 < x < 1: **) g” + Ag 0, y(-1) 0, y(1) = 0 (a) Find all positive eigenvalues for (**). (b) For each positive eigenvalue In, find a correspoding eigenfunction yn(x).
and 3. Find the eigenvalues and eigenfunctions for the given boundary-value problem. There are 3 cases...
and
3. Find the eigenvalues and eigenfunctions for the given boundary-value problem. There are 3 cases to consider. g" + Ag = 0 y(0) = 0, y'(%) = 0 8. Given the initial value problem (3 – 4 g" + 2z +174 = In , g(3) = 1, y'(3) = 0, use the Existence and Uniqueness Theorem to find the LARGEST interval for which the problem would have a unique solution. Show work.
the below is the previous question solution: 1. Recall the following boundary-value problem on the interval [0, 1] from...
the below is the previous question solution:
1. Recall the following boundary-value problem on the interval [0, 1] from Homework 2: f" =-Xf, f'(1) =-f(1). f(0) = 0, Show that if (Anh) and to this boundary-value problem, λι, λ2 〉 0, λιメÂn then fi and f2 are orthogonal with respect to the standard inner product (.9)J( gr)dr. (You may use the solution posted on the course website, or work directly from the equation and boundary conditions above.) (λ2'J2) are two...
Consider the following boundary value problem,
x2y′′ + 17xy′ + (64 +
λ) y = 0, y(1)
= 0, y(e6 ) = 0
(a)
Find the eigenvalues.
(b)
Find the eigenfunctions. Take the arbitrary constant (either
c1 or c2) from the general
solution to be 1.
Consider the following boundary value problem, xy" + 17xy' + (64 + 2) y = 0, y(1) = 0, yle) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either...
#2 ONLY PLEASE
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouville form: do Given a(z), 3(2), and 7(2), what are p(x), σ(x), and q(x) 2. Consider the eigenvalue problem (a) Use the result from the previous problem to put this in Sturm-Liouville form (b) Using the Rayleigh quotient, show that λ > 0. (c) Solve this equation subject to the boundary conditions and determine...
3. (10 Points, part III) Consider the Sturm-Liouville differential equation where the coefficients p(z), q(z), and σ(z) are real and continous on la, b , and p(2) and σ(z) are strictly positive for all a,b (a) Derive the Rayleigh quotient λ from (2). b) What does this quotient describe? Give two examples of applications for this formula. (c) what are the neces,ary conditions for λ > 0 to be satisfied? (d) Recall that the minimum value of the Rayleigh quotient...
Consider these two boundary-value problems: Show that if x is a
solution of boundary-value problem,...
clear steps and brief explanation please
7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution of boundary-value problem ii, then the function y(t) - x((t- a)/h) solves boundary-value problem i, where h b- a.
7. Consider these two boundary-value problems: . x-f (t, x, x') x(a)ax(b) B Show that if x is a solution...
4. Consider the following initial value problem of the 1D wave equation with mixed boundary condition IC: u(z, t = 0) = g(x), ut(z, t = 0) = h(z), BC: u(0, t)0, u(l,t) 0, t>0 0 < x < 1, (a)Use the energy method to show that there is at most one solution for the initial-boundary value problem. (b)Suppose u(x,t)-X()T(t) is a seperable solution. Show that X and T satisfy for some λ E R. Find all the eigenvalues An...
The answer is given. Please show more detailed steps, thank
you.
3. Consider the eigenvalue problem 1<x<2 dx2 y(1)=0,y(2) = 0. dx iwrite it in the standard Sturm-Liouville form. ii) Show that 0 by the Rayleigh Quotient. dx p(x)-x, q(x) = 0, σ(x)-1 According the Raileigh Quotient Any eigenvalue is related to its eigenfunction φ(x) by - x p(x) dr Since the B.C. are ф(1)-0 and ф(2-0, so dx
3. Consider the eigenvalue problem 1
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
3. Consider the boundary value problem for y(x), -1 < x < 1: **) g” + Ag 0, y(-1) 0, y(1) = 0 (a) Find all positive eigenvalues for (**). (b) For each positive eigenvalue In, find a correspoding eigenfunction yn(x).
and
3. Find the eigenvalues and eigenfunctions for the given boundary-value problem. There are 3 cases to consider. g" + Ag = 0 y(0) = 0, y'(%) = 0 8. Given the initial value problem (3 – 4 g" + 2z +174 = In , g(3) = 1, y'(3) = 0, use the Existence and Uniqueness Theorem to find the LARGEST interval for which the problem would have a unique solution. Show work.
the below is the previous question solution:
1. Recall the following boundary-value problem on the interval [0, 1] from Homework 2: f" =-Xf, f'(1) =-f(1). f(0) = 0, Show that if (Anh) and to this boundary-value problem, λι, λ2 〉 0, λιメÂn then fi and f2 are orthogonal with respect to the standard inner product (.9)J( gr)dr. (You may use the solution posted on the course website, or work directly from the equation and boundary conditions above.) (λ2'J2) are two...
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