[Second Order Equations] How do you solve question 4? 1. Let x lie in the interval (0, 1). Find u (x, t) so that(a) u satisfies the wave equation utt - c²uxx = 0.(b) u satisfies the boundary condition u (0, t) = u (1, t) = 0.(c) u (x,0) = 0 and u₁(x,0) = x².2. Now do Neumann boundary conditions: Let x lie in the interval (0,1). Find u (x, t) so that(a) u satisfies the wave equation utt – c²Uxx = 0.(b) u satisfies the boundary condition ux (0, t) = Ux (1, t) = 0.(c) u (x,0) = 0 and u₁ (x,0) = x².3. Let x lie in the interval (0,1). Find u (x, t) so that(a) u satisfies the diffusion equation ut - kuxx = 0.(b) u satisfies the boundary condition u (0, t) = u (1,t) = 0.(c) u (x,0) = et.4. Now do Neumann boundary conditions: Let x lie in the interval (0,1). Find u (x, t) so that(a) u satisfies the diffusion equation ut — kuxx = 0.-(b) u satisfies the boundary condition ux (0, t) = Ux (1,t) = 0.(c) u (x,0) = e².

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Answered: 4. Now do Neumann boundary conditions:…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Now do Neumann boundary conditions: Let x lie in the interval (0,1). Find u (x, t) so that (a) u satisfies the diffusion equation ut- kuxx = 0. (b) u satisfies the boundary condition ux (0, t) = ux (1, t) = 0. (c) u (x,0) = ex.