Answered: Show that f(x, y) =(Aekx + Be-kx…

Math

Calculus

Show that f(x, y) =(Aekx + Be-kx )(Ce2ky + De−2ky) is a solution of the wave equation ∂2f/∂y2− 4∂2f/∂x2 =0.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

See similar textbooks

Related questions

Q: 4. z = tan-'(y/x), x = e', y = 1 - et

Q: solve the given wave equation utt(x,t) = uxx(x,t) u(0,t) = u(1,t) = 0 u(x,0) = 0 ut(x,0) = 1…

Q: Show that the u = f (x + ct) + F(x – ct) satisfies the wave equation in one-dimensional space.

A: By doing partial derivatives we can prove

Q: Verify that u is a solution to the equation ugx + Uyy + u zz = 0. u(x, y, z) = e4z+3y cos(5z)

A: Follow the procedure given below.

Q: ди ди ду ду Find the cauchy-riemann equations of, f (z) = | z | sin z. əx' dy'dx' ðy,

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1. In…

Q: Show whether the following functions are wave functions or not. 1. У(х, t) 3D А exp(ikx) = A- exp…

A: A wave function is a function which can be expressed in the form yx,t=fkx±ωt where the function fu…

Q: The magnetic field along a solenoid is conservative and given by 2xy 7- (2 x ₁-2x, (x²+1)-2). ¡−2x,…

A: Given a vector field as F=2xyx2+1-2x,lnx2+1-2 We need to find the scalar potential from which this…

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x Y F(x, y) =

A: To find the work done by the force field F in moving an object from P-3, 7 to Q7, 5. Fx,…

Q: Show that the field F = (cos x)i + (- y sin y)j + (z3)k is conservative and Önd a potential function…

A: F = ( Cosx )i + ( -y Siny )j + ( z3 )k F = gradient ( - Sinx - y Siny - Cosy + z4/4 ). Thus, we can…

Q: 2. Calculate the directional derivative of the scalar field U(x, y,z) at the point M,, along the…

A: Given that : U=xz3y-x3y=xz3y-x32y12 The gradient will be calculated as :…

Q: Consider the wave equation Uzz, 0 < x,t < T, u (7, t) = 0,0 < t< n Utt u (0, t) Find the maximum of…

Q: An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0 0, at2 əx²…

A: Let us consider the wave equation ∂2u∂t2=∂2u∂x2, 0≤x≤1, t≥0 and L=∆x=0.25; K=∆t=0.1 Consider x=ih…

Q: Solve the wave equation in two dimensions Utt = v²u u (x, y, 0) = sin 4y U (x, y, 0) = cos xcos3y…

Q: Use the vectorized Euler method with h=0.5 to find an approximation for the solution to the given…

Q: Calculate the work done by the vector field F(x, y)= ,2xy) on a particle that moves once around the…

Q: { e, a| 1, The Fourier integral of f (x) = %3D A) roo w sin w-cOS w sin zwdw w2 roo sin w-CoS W sin…

Q: EXERCISE 5. Show that the function (c?t² – a² – y? – z²)-1 is a solution to the three dimensional…

Q: Solve the wave equation on the half line with the Utt – cʻuxx = 0, x> 0, t > 0 и, (0, 1) %3D h(),…

A: Given the wave equation is utt-c2uxx=0, x>0, t>0ux(0,t)=h(t),…

Q: Find a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y)

A: we have to find potential function.

Q: 3. Verify that u(r,t) = sin(r - at) satisfies the wave equation:

A: To verify that ux, t=sinx-at satisfies the wave equation ∂2u∂t2=a2∂2u∂x2

Q: Show that the function f(x, y, z) = x² + y? – 2z² satisfies the Laplace equation.

Q: Find a potential function for the vector ficld F(x, y, 2) = 3x²i j| 2z In yk. %3| A) r3 + 2z ln y +1…

Q: Solve the wave equation using Fourier Transform: ou o'u , -∞0 %3D u(x, 0) = 0 u, (x, 0) = e 23| O a.…

Q: 1. Use isoclines to sketch the direction field for y' = x+ 2y and sketch the solution curve that…

Q: Obtain the solution of the wave equation u 12 under the following conditions (i) u(0, t) = u(2, t) =…

Q: Given a scalar function V(x, y) =-(x² +y² ), the directional derivative of V in the direction of the…

Q: Identify the work done, J. F.dr by an electric field, E = (x + xy)î + (y + 5)f – 5zk V/m to move an…

A: Work done along the curve C by vector field F . Where C is given by parametric equation r(t)…

Q: (a) Consider the 1-D wave equation Utt = Uxx u(0, t) = u(1, t) = 0, t>0 0<x< 0.2 u(x, 0) = { х, l0.2…

A: Separate the wave equation into ordinary differential equation, Substitute

Q: Verify that the function u(x, t) = (r – at)° + (x + at)° satisfies the wave equation uu =

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5

A: We can solve this using by draw a graph

Q: Show that the vector field F = i + sin(z) j + y cos(z) k is conservative and then find the…

Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

Q: Find the work done by the force field F(x, y) = xi + 2yj on a particle moving along the path C:x =…

Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

Q: The work done in moving a particle in the force field F= x- i+ 3xy j from (0,0) to (1,2) along the…

Q: If F = (4xy – z³) î + 2x² ĵ – 3xz² k is a conservative force field, then scalar potential of F is…

Q: Solve using wave equation: u(0, t) = u(π, t) = u(x, 0) = 0, du/dt | t = 0 = sin(x)

Q: A path C is defined by the parametric equations z(t)=t, y(t) = 2t, 0<t<1, and a vector field is…

A: It is given that a path C is defined by the parametric equations x(t)=t, y(t)=2t, 0≤t≤1 and a vector…

Q: Exercise 5: Solve the following nonhomogeneous wave equation Uu(x, t) = uzz(x, t) – 9, t>0, 0 <x<1…

Q: Find the work done by the force field F in moving an object from P(-4, 8) to Q(6, 4). F(x,y) = 2* 1…

Q: Find the work done in moving a particle in the force field F = (2r + y)i + (3y – 2)j along the…

A: Work done in moving a particle in the force field along along the curve C is: ∫CF→·dr→ here F→ is…

Q: u(0,t)=0 2. Consider a piano string of length L = 50cm that satisfies the wave equation Utt81Uxx, 0…

Q: Find the work done by the force field F on a particle moving along the given path. F(x, y) = xi +…

Q: For the particle in a box, show the wave functions w, NTTX sin - for n=3 and n=6 are normalized and…

A: Note that the question has a typo. Since, The function sin(nπx/l) is of period 2l/n.

Q: Consider the wave problem -0 0, J1-r, -1<r < 1, -1 < x< 1, u(r,0) = f(x)= 0, otherwise, du (r,0) =…

A: The given problem is to solve the wave equation partial differential equation with given initial…

Q: 5- Find the solution of the following wave equation using the method of separation of variables.…

Q: Consider the 2nd order equation d²y + Sin dy + y? +y = 0. dt, Choose the right assertion A) the…

Q: let lly):xy"-x (42) y' + (x42)y a. Consider the homogenzous dipperential equation Lcy) = i the t y=X…

Q: 2. Consider the wave y(x,t) = 4 sin (10t - x). Find the correct phasor Y to this wave: A. Y =…

Question

Show that f(x, y) =(Aekx + Be^-kx )(Ce^2ky + De^−2ky) is a solution of the wave equation
∂²f/∂y²− 4∂²f/∂x²=0.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Partial Derivatives$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Find the solution to the wave equation on the half - line: utt = c^(2) uxx, x > 0 , t > 0. u(0,t) = 0, t > 0. u(x,0) = 0, ut(x,0) = e^(-2x), x > 0.
Show that the function z = cos(4x + 4ct) satisfies the wave equation ∂2 z/ ∂t2 = c2 (∂2 z /∂x2 ).
Solve using wave equation: u(0, t) = u(π, t) = u(x, 0) = 0, du/dt | t = 0 = sin(x)
Show that the function z = ln(x + ct) satisfies the wave equation ∂2 z/ ∂t2 = c2 (∂2 z /∂x2 ).
For the wave equation in R3(i.e., (x1 , x2 , x3 ) ∈ R3), let u = u(r, t) be theradial symmetric solution of the systemutt = ∆u, 0 ≤ r < ∞, t > 0u(r, 0) = 1, r ≥ 0ut(r, 0) =2, 0 ≤ r ≤ 1,0, r > 1 Find u(2, 1) and u(2, 2).
Show that the function z = sin(x − ct) satisfies the wave equation ∂2 z/ ∂t2 = c2 (∂2 z /∂x2 ).
Let f(x,t)=cos(12x+4t). Find the value of K so that f satisfies the wave equation ∂^2f/∂x2=K∂^2f/∂t^2
Show that ¥(x,t)= Asin(wt+kx) describes a wave motion
Find u(x,t) from the wave equation, where length of string is L = 1 , c**2 = 1and the initial velocity is zero and the initial deflection is as follows.
Consider the wave equation utt = uxx, (x, t) ∈ R2. find 2 distinct solutions please
solve the one dimensional wave equation with the boundary conditions and inital conditions as given below: δ2u/δt2 = 1/pi2.δ2u/δx2 u(0,t)= 0, t>0. u(1,t)=0, t>0 u(x,0)= sinππxcosπx, 0<x<1 δu/δt(x,0)=0 0<x<1 using the method of seperation of variable
Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.