please help. please be clear and neat
please help. please be clear and neat Consider the following BVP day dy + + \y...
+ dac 1. Consider the following BVP day dy d.x2 + Ag = 0, g(0) = g(2) = 0. (a) Find eigenvalues and eigenfunctions of the problem; (b) Put the equation in self-adjoint form, and give an orthogonality relation; (c) Show that each eigenfunction of the problem can not correspond to two different eigenvalues.
#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...
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...
Please answer all parts of the question and clearly label them. Thanks in advance for all the help. 5. An eigenvalue problem: (a) Obtain the eigenvalues, In, and eigenfunctions, Yn(x), for the eigenvalue problem: y" +1²y = 0 '(0) = 0 and y'(1) = 0. (5) Hint: This equation is similar to the cases considered in lecture except that the boundary conditions are different. Notice how each eigenvalue corresponds to one eigenfunction. In your solution, first consider 12 = 0,...
Consider the following second order linear operator: 82 with Notice, that if instead of 3 we had 2 there, we would get a Legendre operator (whose eigenfunctions are Legendre polynomials). But nothing can be further from it than the operator above. The eigenvalue/eigenfunction problem, emerged in the analysis of vibrations of a particular quant urn liquid. An eigenvalue λ corresponds to an excitation mode of frequency Ω = V The eigenfunction ψ(r) would give a spatial profile of the deviation...
Hello, please help with the following problem - I will give positive rating for fast response! (a) Write down the general form of a SLBV problem including the boundary conditions at the ends (b) Consider the second order boundary value problem -[(1+x?)y'l' = 4y + 1,y(1) = 0, y(0) =0,0 < x 51. Is this a SLBV problem? Explain. (c) Derive the eigenvalues and eigenfunctions of y" + dy = 0, y'(O)= () = y(1)+y'(1) .Is A = 0 an...
5. Consider the problem a2y"y _2.J 0 x1 = 0, y(0) 0, y(1= 0. (a) Put the problem in Sturm-Liouville form and explain the nature of any singular points. (b) State the appropriate modified boundary conditions (c) Find all eigenvalues and eigenfunctions for the modified problem 5. Consider the problem a2y"y _2.J 0 x1 = 0, y(0) 0, y(1= 0. (a) Put the problem in Sturm-Liouville form and explain the nature of any singular points. (b) State the appropriate modified...
Please show working! If unsure of the answer please leave for someone else. Consider the Sturm-Louiville problem d2 y +2y 0 dr2 (0)0, y(3) 0. With n defined as taking values n 1, 2,3, ..., complete the following. (a) Enter the eigenvalues. An = (b) Enter the eigenfunctions Yn Consider the Sturm-Louiville problem d2 y +2y 0 dr2 (0)0, y(3) 0. With n defined as taking values n 1, 2,3, ..., complete the following. (a) Enter the eigenvalues. An =...
Please answer the following correctly and write neat and clear For the RL circuit given, find the differential equation relating the output y(0) to the input x(o). 2 i(t) L-IH va 3 For the RLC circuit, given, find the differential equation relating the output y) to the input x(0) y(0) R-0,5QC-IF し-0.SH /2 d t 孔 d t
Please help (1 point) In this problem we consider an equation in differential form M dx + N dy-0 (- (xy' +y)) dx + (- (x2y + x))dy 0 Find If the problem is exact find a function F(x, y) whose differential, d F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE otherwise find F(x,...