Please solve following wave equation on [-1,1] utt(x,t) = uxx(x,t) u(−1,t) = 0 u(1,t) = 0 u(x,0) = f(x) ut(x,0) = g(x) Only have to discuss the case lambda > 0
Q: Exercise (3-2): find Fourier series Question (1) f(x)=x/2
A: To find the Fourier series expansion of fx=x2 Fourier series expansion for the function fx on the…
Q: Question 1. Given a metric space . (a) If 2, y E X and p(x, y) 0, prove that a y. (b) Prove that a…
A:
Q: 3. Given an equation x1 + x2 + x3 + x4 = 16. How many solutions are there with conditions as below?…
A: The given problem is to find the number of integral solutions for the given equation under the given…
Q: For each of the following, use Euler's Formula to find the missing value for each polyhedron. A) 4…
A:
Q: (j4+43)(20js (-35°)" 2cjs et @= Simplify o and write it in rectan 763 (32çis40°)
A:
Q: a. Find a reduced residue system modulo 15. b. Find the multiplicative inverse of each residue.
A:
Q: Use Lagrange multipliers to find the maximum volume of a box inside a sphere of radius 12cm. -Make a…
A: Let dimension of box be,height = x, width = y, lenght = z Where x, y, z ≥ 0and equation of sphere…
Q: 8. Suppose a certain bond sold a volume of 2, 375, 000. If the bonds sold for $824.99, calculate the…
A: Solution :-
Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…
A: Introduction: When we apply force 'F' to a block, the body accelerates or speeds up or down…
Q: Three numbers a, b, c are such that a< b< c. The median is 12, the range is 12 and the mean is 14.…
A:
Q: Consider f(x) = 4.4x³ + 1.1x2 - 5.4x + 8.6. Using the given function, approximate f(2) by making use…
A:
Q: A certain bacteria culture is observed to double its amount after two hours it was initially…
A:
Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…
A:
Q: Find r'(t), r(t,), and r'(t,) for the given value of to- r(t) = (5 + t)i + t°j, to = 1 r'(t) = r(t,)…
A: To find r'(t) and to sketch the curve represented by a vector-valued function and sketch the…
Q: 7 dx x2 + 4x + 8 00
A: ∫-∞∞7x2+4x+8dx
Q: 2. The sum of the digits of a four-digit number is 23. The ones digit is 4 times the thousands…
A:
Q: Find the volume of the solid that lies within both the cylinderx + ye = 1 and the sphere x +y + 2 =…
A:
Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…
A: The formula for percent error is: PE = (|Estimated value-Actual value|/ Actual value) × 100 Or…
Q: Show whether or not the following limit exists: xy³ lim (x,y)→(0,0) [x2 + y6
A:
Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.
A: Solution
Q: Colcul.ate and simplify the Wronokian: w Cez^sinx -2X -2X cosx)
A:
Q: Diagonalize the following matrix, if possible. 10 -2 Select the correct choice below and, if…
A:
Q: Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider…
A: We have to evaluate limx→∞3x−23x+53x+1. If we substitute the limit then we will get 1∞, which is…
Q: Question 7. Prove or disprove: (a) The union of two subgroups of a group (G, *) is a subgroup of G.…
A:
Q: For the figure, do a dilation centered at the origin with a scale factor of -. Then answer each…
A: a) Longest side of orignal figure is 8 units. Now after dialation with scale factor of 14, longest…
Q: solution of the diffe d x; y(1) = 0, d:
A:
Q: 10. Three circles of radii 115, 150, and 225 m are tangent to each other formed by joining the…
A: Solution
Q: Question 2. functions f : [0, 1] → R. Define an integral norm || · ||i by Let C[0, 1] represent the…
A:
Q: Barcode A can be successfully read with modules as small as 0.31mm. Barcode B can be successfully…
A:
Q: (a) Find the run, rise, and slope given by triangle ABC. rise: ] slope: ] run: (b) Find the run,…
A: To find the run, rise, and slope of given triangles.
Q: The average value of the residuals is
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: The complex number z is defined by z = 3 -z+4·j where z is real. a) Find, in terms of z, the real…
A:
Q: How many random errors of magnitude plus of minus one would be necessary to have 35 different ways…
A:
Q: 4. The diagram shows the point A(-5, -6, - 1) a) Name the coordinates of the points B. G D. G b)…
A: From the given figure where OD=1 unit in negative direction along z-axisOF=5 unit in negative…
Q: United Metal, Inc., produces alloys B1 (special brass) and B2 (yellow tombac). B1 contains 50%…
A:
Q: {m eN:4| m}
A:
Q: find Fourier series [o, 2w] an <x<π fcx) = TくXく 2w
A:
Q: rind the Euler Circuit on this graph using Fleury's algorithm, starting at vertex A.
A: Find the Euler Circuit on this graph using Fleury's algorithm, starting at vertex A.
Q: Suppose p and q are distinct prime numbers. Find the number of positive integers r < pq such that…
A: We use Exclusion - Inclusion principle to solve this problem.
Q: For the matrix, list the real eigenvalues, repeated according to their multiplicities. 6 -2 0 8 0 6…
A: An eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes…
Q: Use the graph of gxgiven in the figure below and the fact that g(0) = to select the correct graph of…
A: Given,Graph of g'(x) and g(0)=50 To find: Graph of g(x) Coordinates of all critical and…
Q: luate the triple integral /// V² + y² + z² dV over the spherical shell E 9.
A: Integration using spherical coordinates
Q: Given that the acceleration vector is a (t) = (-9 cos(3t), –9 sin(3t), 5t), the initial velocity is…
A: Introduction: Suppose, the position vector that represents the position of a particle at any moment…
Q: Evaluate the line integral by the two following methods. f (x - y) dx + (x + y) dy C is…
A:
Q: Evaluate the limit. lim -5 V-I-2
A: We have to find value of given Limit.
Q: 8. In the prism, assume all dimensions have different lengths. a. State 3 equal vectors to DC. b.…
A: The 3 equal vectors to DC→ are HG→, EF→ and AB→ Since they have same magnitude and the same…
Q: Determine the vector field of F. F(x, y) 3D yi — хј
A: Let us make a table to draw the vector field as shown in the image below.
Q: Solve the ordinary differential equation y'=1+y^2 ,y(0)=0,x1=1/4
A: Given ordinary differentiation equation is y'=1+y2, y0=0. Simplify y'=1+y2, we get…
Q: Find the positive root in 4th iteration of the equation xeX-3 in the interval [1,2] using Regula…
A: We have to find the positive root in the 4th iteration of the given equation in the interval 1,2…
Q: Q1: Find partial derivatives of the function with respect with each variable 3) f(x, y) = (xy –1}…
A: Solution
Please solve following wave equation on [-1,1]
utt(x,t) = uxx(x,t)
u(−1,t) = 0
u(1,t) = 0
u(x,0) = f(x)
ut(x,0) = g(x)
Only have to discuss the case lambda > 0
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
- This is a classical wave equation problem and I am struggling with the integration part of it. we have a string fixed on both ends and a velocity profile at time 0 where v= (2v0/L) x from 0 to L/2, and (2v0/L)(x-L) from L/2 to L. Picture attached is the integration I'm struggling with.State the solution formula for the Cauchy problem for the homogeneous wave equation on R3. Prove that solutions corresponding to a localized initial signal (i.e. initial position and derivative are supported in a small ball) have a wave fore front and a wave back front and that these fronts are close to each other. Conclude that music is possible in R3. Say in words what happens if we consider R2 instead.this question subject is PDE (partial differential equation) and the minimal surface is elliptic
- This is for PDE CLASS. Pease TYPE your solution. Verify that your solution indeed solves the wave equation and satisfies the given initial conditionsFind the solution of the threshold problem in the next wave equation by the variable separation method.13. The standard form of 3dy-xydx = 3y3e4x/3 by Bernoulli's equation is:
- Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete and Step by step solution please)Using the Fourier transform, prove that the solution to the wave equation utt = C²uxx with the initial conditions u(x, 0) = f(x) and ut (x, 0) = g(x) is :What does Cauchys EU theorem guarantee for The IVP: dy/dt = -(y)^2/2t, IC: (to,0)
- True or False The following systemdx/dt = − cos x sin ydy/dt = 2x^2 + sin x cos yis a Hamiltonian system.solve the wave equation ut+ux=0 on a digital computer using Lax Scheme and Lax-Wendroff schemeThe technique that we used to solve the time-dependent Schrodinger equation in class is known as separation of variables. Use the same technique to investigate solutions of the wave equation: ∂2y(x,t)∂x2=1v2∂2y(x,t)∂t2