1010. Solve the wave equation a² = for 0 0 subject to the boundary conditionsazu%3Dat2ax2u(0,1) = 0, u(1,1) = 0 and the initial conditions u(x,0) = 0.05 sin 47x, | t=0 = 0. Simplify your answer.vioe.e

Given Wave equation: a2∂2u∂x2=∂2u∂t2 for 0<x<1 and t>0 Given Boundary conditions: u(0,t)=0,…

Answered: 10. Solve the wave equation a2 d*u ax2…

10. Solve the wave equation a2 d*u ax2 azu for 00 subject to the boundary conditions at2 au u(0,1) = 0, u(1,1) = 0 and the initial conditions u(x,0) = 0.05 sin 4nx, It=0=D0. Simplify your answer. at

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Solve the Following Euler's (or Cauchy's) Equations: (1) x'y" – 2x² y" – 2.xy'+ y =0

A: As per our guidelines only first question will be solved.

Q: t(+²-3) x² = C X x³ + (t²-3) = C₁ practice Problem: dy 1) (2²4-y) casx du = ~ Sinax वर e 2) dy…

Q: Find in the parametric equation d'y dx² x = 5 sin² t y = 2 cost 0≤t≤ 2π.

Q: 3. (D'+ 9) у -D0 %3| Ans. y=c, sin 3x+c, cos3x

A: See below the answer and explanation

Q: 1. Classify the D.E. 2xe dx + (x²e + 1)dy 0.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: Find dy/dx and d^2y/dx^2.

A: Given

Q: Solve the wave equation using Fourier Transform: o'u ou - ∞ 0 %3D -12x utx, 0) = H(x)e u, (x, 0) =…

Q: 1) Solve the IVP: y" + 2y' + 2y = 5 sin t + 5 cos t : y(0) = 1 and y'(0) = 2

A: Given initial value problem is y''+2y'+2y=5sint+5cost, y(0)=1, y'(0)=2. Let y'=dydt=Dy and…

Q: 4. Consider a vibrating string of length L = T that satisfies the wave equation Pu Pu t > 0. 0 <x <…

Q: Find dy/dt. 11) y = (ecost/9)4 A) cos e4 cos(t/9) B) sin e3 cos(t/9) e4 cos(t/9) D) - (esin(/9)3

A: Use the chain rule of derivative and simplify.

Q: S(2) = e- f(2): cos 2ry+ie sin 2ry 2. Find the cauchy-riemann equations of rau du dv dv ləx'əy'əx'…

A: Find partial derivative with respect to x and y. Comparing real and Imaginary part find u and v.

Q: 10.3 Show that the setdown under a standing wave system is a?k 7(x) = (cosh 2kh cos 2kx – 1) 4 sinh…

A: Answer is mentioned below

Q: A solid concrete porch consists of 3 steps and a landing. The steps have a tread of 11 inches, a…

Q: Practice Problem: dy 1) (2²8-4) carx dx = et sinax -у) сах sets वर

A: Here we have to solve the differential equation (e2y-y)cosxdydx=eysin2x.

Q: 4+t -1 -1 3 y + t· sin "(2t) - 5[tan (6t)]° + cosh(t) + 4ln t. 3t te dy Find:- -.Don't simplify your…

Q: (a) Solve the inhomogeneous 1st order equation Uz - Ut = cos t U(x, 0) = 0.

Q: PART 1: State the characteristics (order, degree, type) of the given DE. 1. (1-x)y" - 4xy' + 5y =…

Q: (3 = 3²), and find u(x,t) for the following wave: and Solve the wave equation (²) u(0,t) = u(1, t) =…

Q: 7. Find the first derivative of y with respect to x of the following parametric equations. x = 1 +…

Q: 2) Solve the given Variable separable DE 1) x cos² y dx + tany dy =0

Q: (a) Solve the following inhomogeneous wave equation on the real line Utt-c²Urr = 2x - sin r U(x, 0)…

Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

Q: (a) Solve the inhomogeneous 1st order equation Uz - Ut = cos t I U(x, 0) = 0.

Q: 1. y = 5u°; u=7x – 4x' + 2x –9 2х-9 u +1. u=Vx? +1 y = u? -1' 3. x=7y -3y +y +8 2.

Q: Which of the following is not linear ? y" xy" + 3 = T y" + 3y' + 2u = (sin 7) 2'y" + ry' + 4y = e…

A: We will solve the problem

Q: Solve the wave equation for the following cases: ii) For free free ends beam with following…

Q: - (D' - 4)y = x'e"

Q: If simple harmonic motion is described by æ(t) = (/2/2) sin 2t + ø, the phase angle is when x(0) =…

Q: Nitin

A: (a) y(t)= ±5.83 cos(3t-30.96o)(b) Time period of the motion = 2.09 s Frequency of the motion =…

Q: he equation dy dx (r,0) econd derivative is r = 60, = f'(0) sin 0 + f(0) cos 0 f'(0) cos 0 -f(0) sin…

Q: A suspension bridge swinging in the thunderstorm can be modelled by the following equation:…

Q: Show that xo 0 is a regular singular point of the equation %3D xy" + + x ) y' – 4y = 0. Determine…

Q: 2 5 -2 0 ū' = Au where A

Q: Solve the inhomogeneous wave equation on the real line Utt − c 2Uxx = sin x, x ∈ R U(x, 0) = 0,…

Question

10
10. Solve the wave equation a² = for 0 <x<1 and t> 0 subject to the boundary conditions
azu
%3D
at2
ax2
u(0,1) = 0, u(1,1) = 0 and the initial conditions u(x,0) = 0.05 sin 47x, | t=0 = 0. Simplify your answer.
vioe.e

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

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, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

The equation, d(t) = 255t + 5654 represents the tuition, d dollars, at a college for the year Find an inverse that is t years since 2002. function for this model. t-255 5654 t+5654 255 t-5654 255 t +255 5654
Determine dy/dx of y = 3x(sin(2²/2)) None of the choices Ocos()+sin() O=sin() + 3 cos (2) -12 O² cos()+3 sin (2)
Need help with the following problems: 1. Solve this differential equation: e^t (dy/dt) = y^2, y(0) = -1/4 2. Consider the parametric equations x = −3 sin θ, y = 4 cos θ, 0 ≤ θ ≤ π. Sketch the curve represented by the parametric equations. Describe the motion of a particle with position (x, y) as θ varies in the interval [0, π]. 3. A bacteria culture starts with 60 bacteria and grows at a rate proportional to its size. After 2 hours there are 300 bacteria. Find an expression for the number of bacteria after t hours. When will the population reach 2000?
1. dt² dy +6. +8y=-4 cos(3t) dt 2. d²y dy +4 dt² dt + 13y = 3 sin(2t)
Find the general solution: y" + 5y' + 6y = 4e¬t cos2t + sin2t A - B I
Q1:- Solve the following DEs:- xy2-cos x sin x 1) y' У(1-x?) 2) (-4y + e-3*)dx = 4 dy dy 3) + 2x³y = y³x3 dx dy 2 4) 2xy = x + y? + 1 dx
Given the function f(x) = x²-5x+2, find the value of the derivative at x = 2, f(2). A 7 B 3x2-5 C) 2 D 8
Solve the wave equation 1 8Pu Uz(0, t) = u#(1, t) = 0 4 dx2* Pu u(x, 0) = x(1– x), Ut(x, 0) = sin(3Tx).
4) Determine whether the given set of functions is linearly independent on the interval (-x,). a) (z) = cos 2z, (2) = 1, 1,()= cos z b) (z)=z, 1,(2)=z-1, (z)=z+3 c) ()=e**, 1,(=)=e
7. Show that the equation f(x, y) = sin(x + y) + cos(x - y) satisfy the wave equation 0²1 01-01-1 dy² 0
2 3. If tan(a-iß) = x-iy, show that x² + y° - 2ycoth2B = -1 -1
1. Differentiate F(t) = e4t³ sin 2t [Hint: y = e", u = 4t³ sin 2t.]