Using Green's functions to solve wave eqn problem

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

Study Guide 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 Please see attached for all other questions.

LaPlace Transformations with some Initial Value 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... a inverse-square central force field. Show that... Please see attached for the rest of this question, and all other questions.

second order homogeneous differential equations

Consider the homogeneous second order equation: d²y/dx² + 5.dy/dx + 6y =0 a) using the substitution u = dy/dx +3y, derive a first order differential equation connecting u and x. find the general solution of this equation and use it to solve the original equation, obtaining the general solution. b) Repeat the procedure of (a) using the substitution v = dy/dx +2y. c) By considering that the two solutions obtained in (a) and (b) both satisfy the differential equation independently, deduce the most general solution. By generalising the coefficient of x in the solutions to (a) and (b), we can obtain an 'experimental' solution of the form y = Ae^λx, where λ is a consta... click for more

Classification/Solve PDE

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 arguments.