Please give me detailed, step by step hints to solving the problems. Thanks very much!
Please see attachment for complete questions (for the below "..." indicates equation to be found in attachment). Thanks! (a) Write down the Fourier (sine) series solution u(x,t) of the wave equation ... on the interval ... satisfying the boundary conditions ... and the initial conditions ... (b) Use the identity ... to sh ...continues
Polar Coordinates; Laplace's Equation; Boundary Conditions; Wedge Domain
I need some clues on figuring out these questions. Please see attachment for complete problems (regarding the below: "..." indicates an equation to be found in the attachment. Thanks!) (a) Using polar coordinates, find all the separated solutions of Laplace's equation satisfying the attached boundary conditions in the "wedge ...continues
Heat Equation; Boundary Conditions; Steady State Condition; Initial Value Problem
(a) Find all the separated solutions of the attached heat equation (satisfying the attached boundary condition) (b) Use these separated solutions to write a series solution for the initial value problem posed by the attached pde and the attached boundary conditions, with the initial condition given by {see attachment} (c) ...continues
Wave Equation on Semi-Infinite Domain (Neumann BC) - Dirichlet and Neumann conditions
Dirichlet and Neumann conditions Solve the following PDE explicitly in terms of...and...in each region...and...: Please see attached for full question.
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
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 ...continues
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 ...continues
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
