Solve Helmholtz Equation : Bessel's Equations
a)Solve the Helmholtz equation when u is a function of r only in 2-D. b)Solve the Helmholtz equation when u is a function of r only in 3-D. (see attachment for full question)
Laplace Equation with Neumann Boundary Condition on a Circle
Solve by using series representation and summing the series to get a Poisson integral formula for this Neumann boundary condition problem. Please see the attached file for the fully formatted problems.
Fundamental Solution of N-Dimensional Laplace equation
Please see the attached. The fundamental solution of the n-dimensional Laplace equation solves , (1) where is the n-dimensional delta function. a. Show that if , the solution of the above equation (1) for is , where is a constant. b. Use the n-dimensional Gauss theorem to evaluate the ...continues
Dipoles, Quadrupoles and Laplacian : Limiting Potential
Consider a dipole of strength D, oriented along the x-axis and located at the point x =E/2 , y = 0, z = 0, and a dipole of strength –D, oriented along the x-axis at the point x = - , y = 0, z = 0. Write the expression for the potential for these two dipoles. Take the limit as , and show that the limiting potential is given ...continues
given that y=x is one solution, find a second linearly independent solution
(x^2 - x + 1)y" - (x^2 + x)y' + (x + 1)y = 0
Fourier Sine and Cosine Series, Laplace's Equation and Wave Equation
Please assist me with the attached Fourier Series problems. Please see the attached file for the fully formatted problems.
Initial-Value Problems, Wronskian and Particular Solutions (5 Problems)
1. Solve the IVP y'' - 2y' + 2y=0; y(0) = 0; y'(0) = 5. 2. y'''+9y'=0; y(0)=3;y'(0)=-1;y''(0) =2 Please see the attached file for the fully formatted problems. Please give me detailed, step by step hints to solving the problems. Thanks very much!
Fourier Sine Series Solution - Wave Equation, Interval and Boundary Conditions
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 and 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
