Question

In: Math

Problem #2: Use separation of variables with λ = 36 to find a product solution to...

Problem #2:
Use separation of variables with λ = 36 to find a product solution to the following partial differential equation,

y
2u
∂x2
 +  
∂u
∂y
 =  0

that also satisfies the conditions u(0, 0) = 9 and ux(0, 0) = 4.

Solutions

Expert Solution



Related Solutions

Use separation of variables to find a series solution of utt = c 2uxx subject to...
Use separation of variables to find a series solution of utt = c 2uxx subject to u(0, t) = 0, ux(l, t) + u(l, t) = 0, u(x, 0) = φ(x), & ut(x, 0) = ψ(x) over the domain 0 < x < `, t > 0. Provide an equation that identifies the eigenvalues and sketch a graph depicting this equation. Clearly identify the eigenfunctions
Problem #1 : Using separation of variables and the formalism demonstrated in class, find the general...
Problem #1 : Using separation of variables and the formalism demonstrated in class, find the general solution to the Helmholtz equation (also known as the time independent wave equation) : ∇^2 F + k^2 F = 0 Assume that k is a real number. For clarification, the general solution is the solution in the case where boundary conditions are not specified. Problem #2 : Express the following functions as an infinite Fourier sine series using sin(nπx/a) a)f(x) = x b)f(x)...
Determine the solution of the following initial boundary-value problem using the method of separation of Variables...
Determine the solution of the following initial boundary-value problem using the method of separation of Variables Uxx=4Utt 0<x<Pi t>0 U(x,0)=sinx 0<=x<Pi Ut(x,0)=x 0<=x<Pi U(0,t)=0 t>=0 U(pi,t)=0 t>=0
Find the values of λ (eigenvalues) for which the given problem has a nontrivial solution. Also...
Find the values of λ (eigenvalues) for which the given problem has a nontrivial solution. Also determine the corresponding nontrivial solutions​ (eigenfunctions). y''+2λy=0; 0<x<π, y(0)=0, y'(π)=0
Use the separation of variables method to solve the following problem. Consider a long, narrow tube...
Use the separation of variables method to solve the following problem. Consider a long, narrow tube connecting two large, well-mixed reservoirs containing a small concentration of N2 in another inert gas. The tube length is L = 100 cm. To establish an initial concentration profile in the tube, each reservoir is held at a fixed concentration: Reservoir 1 contains no N2 and reservoir 2 has 2 × 10−6 mol/cm3 of N2. (a) At t = 0, the concentrations of the...
X and Y are independent Exponential random variables with mean=4, λ = 1/2. 1) Find the...
X and Y are independent Exponential random variables with mean=4, λ = 1/2. 1) Find the joint CDF of the random variables X, Y and  Find the probability that 4X > Y . 2) Find the expected value of X^3 + X*Y .
Use the method of Undetermined Coefficients to find the solution of the boundary value problem x^2...
Use the method of Undetermined Coefficients to find the solution of the boundary value problem x^2 y '' + y' + 2y = 6x +2 y(1) = 0 y(2) = 1
Let X1,...,Xn be exponentially distributed independent random variables with parameter λ. (a) Find the pdf of...
Let X1,...,Xn be exponentially distributed independent random variables with parameter λ. (a) Find the pdf of Yn= max{X1,...,Xn}. (b) Find E[Yn]. (c) Find the median of Yn. (d) What is the mean for n= 1, n= 2, n= 3? What happens as n→∞? Explain why.
If X and Y are independent exponential random variables, each having parameter λ  =  6, find...
If X and Y are independent exponential random variables, each having parameter λ  =  6, find the joint density function of U  =  X + Y  and  V  =  e 2X. The required joint density function is of the form fU,V (u, v)  =  { g(u, v) u  >  h(v), v  >  a 0 otherwise (a) Enter the function g(u, v) into the answer box below. (b) Enter the function h(v) into the answer box below. (c) Enter the value...
Using the method of separation of variables and Fourier series, solve the following heat conduction problem...
Using the method of separation of variables and Fourier series, solve the following heat conduction problem in a rod. ∂u/∂t =∂2u/∂x2 , u(0, t) = 0, u(π, t) = 3π, u(x, 0) = 0
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT