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Problem 2 Use the method of separation of variables to compute the solution of SEE NEXT...
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
3. Use separation of variables to compute the first five terms of the series solution of the IBVP: urr (r,0) + r-rur (r, θ u (1,0, t) 0, u (r, θ, t) , ur(r, θ, t) bounded as r-+0+,-π < θ < π, t > 0, u (r,0,0) = r sin θ, ut (r.0, 0) = 0, o < r < 1, -π < θ < π. Hint: Follow the example from Lecture 19 and use the fact that with...
2. Use the method of separation of variables to solve the boundary value problem ( au = karu 0<x<L t > 0 (0,t) = 0, > 0 (1.1) -0. > 0 (u(a,0) - (x) 0<x<L. Be sure to detail exactly how f(x) enters your solution E-
Use the solution of the vibrating string with fixed ends obtained with separation of variables to solve the following initial boundary value problem on the interval [0,1], and sketch the solution for t 0, t= 1/2 and t 1. ial diffe au u ot2 x x<1, t>0, u(x, 0) f(x)-sin zx, (x, 0) 0, u(0,)=u(1,t)= 0
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
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.
Problem #4: Use separation of variables to find a product solution to the following partial differential equation, Ou (5y + 8) ou си + (3x + 6) oy = 0 that also satisfies the conditions u(0,0) = 9 and ux(0,0) = 8. Problem #4: Enter your answer as a symbolic 9*e^(1/9)*(3*x^2/2+6*X-5*y^2/2-function of x,y, as in these examples + 6x - 9e1/9(3 + 52 - 8y) Just Save Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3...
4) (2 marks) Use the method of separation of variables to find the explicit solution of the following equation
(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...