Show that a function w(x, y) = cos(2x + 2ct) satisfies wave equation.
2. Show that the function w = ln(2x + 2ct) is a solution of the one-dimensional wave equation, aw aw at2 Әr2
Show that the function y = cos (ln(x)] satisfies the differential equation 22 day dy +2 dx +y = 0. dc2
P(x,t) = Aeixe-ißt a) Show that the above function is a wave by showing that it satisfies the wave equation. A, a, B are arbitrary constants, i is the unit imaginary number. b) Find the wave speed where a = 1, B = 4, and A-3.
(1 point) Show that the function f(x, y) = ux4 – 2x”y – 18x²y2 + vxy3 + wyt is harmonic, i.e. satisfies Laplace's equation af + əx2 a2f dy2 0 if and only if the constants U, V, w are given by U = V = W =
2. Determine whether the following function satisfies the wave equation. Y(x,t)= Ae (kr-at)
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
A fellow student proposes that a possible wave function for a free particle with mass \(m\) (one for which the potential-energy function \(U(x)\) is zero ) is$$ \psi(x)=\left\{\begin{array}{ll} e^{-k x}, & x \geq 0 \\ e^{+\kappa x}, & x<0 \end{array}\right. $$where \(\kappa\) is a positive constant. (a) Graph this proposed wave function.(b) Determine the energy of the particle if the proposed wave function satisfies the Schrödinger equation for \(x<\)0.(c) Show that the proposed wave function also satisfies the Schrödinger equation...
Given: phi(x,y) satisfies Laplace’s Equation, show that
Psi(x,y)=(x^2+y^2)*phi(x,y) satisfies the biharmonic equation.
x,y) Setisfics satisfies the biharmonic e
2. Determine whether the following function satisfies the wave equation. v(x,t)= 4e(in-a)
Suppose f is a function that satisfies the equation f (x + y) = f (x) + f(y) + xºy + xy2 + xyz + xy for all real numbers x and y. Suppose also that f(x) lim = -1. Find f' (a). Show your work in 30 the PDF version of the test. 2