please answer compleltly 2. Find the eigenfunctions and eigenvalues for the differential equation d^2u(x)/dr^2 = -k^2...
please show work differential equation 1. Find the positive eigenvalues and the corresponding eigenfunctions of the boundary value problem -" +42y = 0; y(0) = 0, y(27) = 0. If the equation has no positive eigenvalues, then state so.
Find the solution of the differential equation that satisfies the given initial condition. du dt 2u 2t + sec?(t), u(0) = -5 U = V2 + tan(t) + 25 X
(1 point) In this problem we find the eigenfunctions and eigenvalues of the differential equation B+ iy=0 with boundary conditions (0) + (0) = 0 W2) = 0 For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + B sin(x)For the variable i type the word lambda, otherwise treat it as you would any other variable. Case 1: 1 = 0 (1a.) Ignoring the...
Find the solution of the differential equation that satisfies the given initial condition. du dt 2u 2t + sec?(6), (0) = -5 U = Vz2+ 2 + tan(t) + 25
Wave equation: (d^2u/dt^2) = 9(d^2u/dx^2) with u(0,t) = u(π,t) = 0 u(x,0) = 3sin4x + 8sin5x, ∂u/dt(x,0) = x, 0 < x < π/2 , π − x, π/2 < x < π.
#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...
Consider the second order partial differential equation du/dt= d^2u/dx^2 +2du/dx+u over the domain x in [0,l) and t>=0. It is given that u(0,t)=u(l,t)=0. Use the method of separation of variables to prove that the general solution with the given boundary condition is u(x,t)= infinity series n=1 bnsin(npix/l)exp(-x-((npi/l)^2)t) where bn is a constant for every n N Hint u(x,t)=X(x)T(t) tnsit te Seind ond partial difertinl cuatan +2n St the dowain e To,e) an Use metod o Separet ion Vaiades to rore...
Find the solution to the heat equation on the infinite domain ∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,0,|x|<1|x|>1.∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,|x|<10,|x|>1. in terms of the error function. Q1 (10 points) Find the solution to the heat equation on the infinite domain azu ди at k -00<x<0, t>0, ar2 u(x,0) (X, 1x < 1 10, [] > 1. in terms of the error function. + Drag and drop your files or click to browse...
25 &27 In Problems 15-28 find the general solution of the given higher-order differential equation. 15 y" – 4y" – 5y' = 0 16. y' – y = 0 y'' – 5y" + 3y' + 9y = 0) 18. y' + 3y" – 4y' - 12y = 0 30 d²u 19. d13 + d²u - 2u=0 dt? d²x d²x an de dt2 4x = 0 21. y' + 3y" + 3y' + y = 0 22. y" – 6y" +...
Problem 1. Consider the wave equation ∂ 2 ∂t2 u = ∇2u with c 2 = 1 on a rectangle 0 < x < 2, 0 < y < 1 with u = 0 on the boundary (fixed boundary condition). Find two independent eigenfunctions um1,n1 (x, y, t) and um2,n2 (x, y, t) with either m1 6= m2 or n1 6= n2 (or both) which have the same eigenvalue (frequency). Problem 1. Consider the wave equation a2 u= at2 v4...