Please write clearly! (a) Using the method of separation of variables, find a (formal) solution of...
olve the following heat problem using the method of separation of variables: lxx 6. S olve the following heat problem using the method of separation of variables: lxx 6. S
both please 1. Use the method of separation of variables find the general (explicit) solution to the differential equation = xcscy dy 2. Find the general solution to the first-order linear differential equation dy ex x + 2y = dx X by finding an appropriate integrating factor. (No credit for any other method). Give an explicit solution. 0
use the method of separation of variables to solve the following nonhomogeneous initial-Neumann problem: Hint: write the candidate solution as are the eigenfunctionsof the eigenvalue problem associated with the homogeneous equation.
4) (2 marks) Use the method of separation of variables to find the explicit solution of the following equation
(a) Solve using separation of variables. (Even if you already know the solution, show how to use separation of variables to find it.) Your solution should have one arbitrary constant. (b) Demonstrate that your solution satisfies the differential equation. You can do all relevant integrals in the problem by algebraic simplification, or with a u-substitution.
part A PART IV. 4. Use the Vibration problem. method of Separation of Variables to find the solution of a String A. Ue (x, t)-0.16us (x, ) 0,0x<8 u(0, t)u(8, t)-0,t0 u(x, 0) = 0 , 0
Q2.PNGA sphere of radius R has a specified potential at it’s surface that is given by: V (R, θ) = kR /epsilon0 (3 cos^2 θ − 1) . a) Using the method of separation of variables in spherical coordinate, solve Laplace’s equation to find the potential inside and outside.of the sphere. Refer to Griffith’s examples 3.6 and 3.7 for the method and on how to ”eye-ball” the coefficients in the general solution. (10 points)Using the continuity equation, find the surface charge density...
cos y 1. Use the method of separation of variables find the general (explicit) solution to the differential equation = xcscy cosydy - x CSC²y dy xoschy cosy Xcsc²y.t dx cosy dy = xoscay.secy dx
(1 poin This problem is concerned with using separation of variables to find product solutions. In particular you will substitute ( separate the variables. Then let - represent the separation constant. Solve the resulting ODEs and find (x,1). 1) X() into the given equation and Use separation of variables to find product solutions of the partial differential equation. Separation of variables gives - P T ' + p = 0, The general solution of T''+pT = 0 is T-Com where...
Find the general solution of the first order partial differential equation using the method of separation of variables. Use the substitution U = XY to solve the boundary value partial differential equation 34x + 2 uy = u for . for u(0,y) = 2e By Use the substitution U = XY to solve the boundary value partial differential equation 3ux +2y = for 3. for u(x,0) = 4e2+ +5e*: