Wave Equation on Semi-Infinite Domain : Dirichlet and Neumann Boundary Conditions

Dirichlet and Neumann conditions Solve the following PDE explicitly in terms of...and...in each region...and...: Please see attached for full question.

Green's Functions, Wave Equation, Heaviside Function and Neumann Boundary Condition

The Green's function for the infinite domain is... where H is the Heaviside function. Use Green's functions to solve the Neumann boundary condition problem... Give explicit formulas for the solution in each region x>t and x

Systems of Ordinary Differential Equations (4 Problems)

Problem 8.1 (Prob. 11, p.251) Solve the following system of equations. { x' = y { y' = -x Problem 8.2 (Prob. 18, p.251) Solve the following system of equations with given initial conditions. { x' = -y { y' = 10x - 7y { x(0) = 2 { y(0) = -7 ...continues

LaPlace Transformations with some Initial Value Problems (8 Problems)

Problem 9.1 (Prob. 29. P. 252) Two particles each of mass m moves in the plane with co-ordinates (x(t), y(t)) under the influence of a force that is directed toward the origin and had magnitude k/(x2 + y2) an inverse-square central force field. Show that mx''=-kx/(r^3) and my''= -ky/(r^3) where r = sqrt(x2 + y2) Problem 9.2 ...continues

Partial Differential Equations

a) Classify and find general expressions for the characteristic coordinates for the equation {see attachment} b) Use the canonical coordinates {see attachment} and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that {see attachments} where F and G are arbitrary functions of their ar ...continues

Partial Diff. Equarion - Initial Value Problem

Solve the initial value problem. Please see attached for full question.

Partial Diff. Equation #2

Please solve the initial value problem. See attached file.

Partial Diff. Equation #3

Suppose that u(x,t) satisfies the diffusion equation... for 00, and the Robin boundary conditions... where k, L, a0 and aL are all positive constants. Show that... is a decreasing function of t. Please see attached for full question.

Partial Differential Equation : Diffusion Equation and Explicit Series Solution

Consider the diffusion equation ut = ku.xx for 0 < < pi and t > 0 with the boundary conditions ux(0, t) = 0 and u(pi, t) = 0 and the initial condition u(x,0) = 1. (a) Find the separated solutions satisfying the differential equation and boundary conditions. (b) Use these solutions to write an explicit series solution to t ...continues

Fourier Series and Convergence

Let f(x) ={0 -pi