C- Solve the wave equations below; 1- Solve the boundary value problem; azy = 4 ax y(0,t) = y(5, t) = 0, i) 5 sin nx, whenn t 0 iverity - Ira ii) = 3 sin 2nx - 2 sin 5nx, whenn t=0
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Q: 3. Solve the one-dimensional wave equation subject to the following conditions: [v(0,1)= 0, v(7,t)=…
A: Please check next steps for the solution.!
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Q: C-Solve the wave equations below; 1- Solve the boundary value problem; a²y azy = 4 əx² at2 y(0,t) =…
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- ) Solve 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.Show that the function Z = sin(wct)sin(wx) satisfies the wave equation5C. Under suitable assumptions derive one dimensional wave equation.
- Please short steps and final answer. Solve the wave equation using Fourier Transform: o'u ou - c0 0 %3D -12x utx, 0) = H(x)e %3D u,(x, 0) = 0. Oa. u (x, t) = Real sin wt (12+iw) %3D 2 я Ob. 1 iwx u (x,t) Real cos wt dw (12+iw) Oc. iwx u (x,1) Real sın wt %3D w (12+iw) Od. 1 u (x,1) = Real cos wt w (12+iw) Oe correct ancue3. Solve the radial wave in R3 with initral data gler) =4-r², Yer)=0 equation = Au U, =4. Consider a wave equation on an infinite line, J²u J²u 9 Ət² əx² = 0. = Find the characteristics though the point (1,3). Draw the domains of depen- dence and influence of the point (1,3).
- Solve the following wave equation using finite difference method. 4fxx = ftt - Given: f(0, t) = 0 and f(1, t) = 0 f(x, 0) = ft(x, 0) = 0 sin(x) + sin(2x) (Ref: Hyperbolic Equation)Solve the Goursat problem: = 0 Utt- c²Uxx u|x-ct=0 = x² u/x+ct=0 = x² nt: Use the formula for general solutions of wave equation on the real line. =6 a"M %3D ulo,t)= M(2,*) = 2 Solue the wave equation, fot all 3 cases.
- Consider the wave equation 0 0, with u(0,1) = 1(xt)= 0, u(x,0) = sin x and =0 at t=0. Then u is= Use variables separation method to solve the wave equation uxxutt. This function is defined on spatial domain 0 0. Subject to boundary conditions: ux(0, t) = u,(a, t) = 0 and initial conditions: u(x, 0) = 0 and u₁(x,0) = f(x)for wave equation, seperation of vairables u(x,t)=X=(x)T(t)