Solve the following wave equation on the interval [0,π] Utt - c²Uxx = 0, x = [0, π] ᏆᏆ Ux(0,t) = 0, U‚t = 0 U(x, 0) = 0, U₁(x, 0) = -12c. cos(x).
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![Solve the following wave equation on the interval [0,π]
Utt - c²Uxx = 0, x = [0, π]
ᏆᏆ
Ux(0,t) = 0, U‚t = 0
U(x, 0) = 0, U₁(x, 0) = -12c. cos(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b6d7e66-7486-4295-b8a4-5509f9324ef5%2F2361cc9e-9dbc-4ac7-9f28-7d214c99a631%2Fzcrqdcp_processed.png&w=3840&q=75)
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- Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)Find 4 dx J-cos(3пx) (ез + 1)dtr.Find the solution of the wave equation when initial velocity equal to 0 and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l-x)/I) when x between (1/2) and (I) the P.D.E. is * c2 dx²
- SolveSolve the inhomogeneous wave equation on the real lineUtt − c2Uxx = sin x, x ∈ RU(x, 0) = 0, Ut(x, 0) = 0.Explain what theory you are using and show your full computations.A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 - 3t) Determine the coordinates of the particle if it travelled 10 units from (cos(4), sin(4),2)
- Determine the 1st and 2nd derivatives of the parametric equation.Compute the derivatives of the given functions. b) [12 cos¯¹2x] d dx c) d) e) f) d. du d dz d dy d dq [4 sec ¹3u] [10 tan-¹2z -1 [6 csc ¹ 4y] [9 cot-¹39] = = = = = G 4. 9- FIFind the solution of the wave equation when initial velocity equal to O and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l- x)/I) when x between (1/2) and (1) the P.D.E. is * dt? dx²
- f(z) = 37° cos(z) f'(z) =Find the value of the derivative dy/dx at t=2π/3 when an object moves according to the parametric equations: x(t) = 2t+sin(2t) and y(t) = 3t−3cos(2t) A) = 3+3√3 / 2-√3 B) = 2 - √3 C) = 3 - 3√3 D) = 1/4 (3 - √3)(b) Solve the inhomogeneous wave equation on the real line Utt-c²Uzz = sin x, x ER U(x,0) = 0, Ut(x, 0) = 0. Explain what theory you are using and show your full computations.