Consider the heat equation Ut = AUxx, a €R>⁰, 00 with boundary conditions ux (0, t) = ux (L, t) = 0, t> 0.

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A: Given u(x,y) on the domain x,y|x≥0, y≤0

Q: Subject to, du at 2²u əx² ‚ 00, ux(0, t) = 0,ux(1, t) = 0,t> 0 u(x, 0) = x - x² 2

A: The given problem is to find the solution for the given heat equation partial differential equation…

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Q: 2. Find the solution of the one dimensional heat equation ди Ət V J²u 0 < x <L, მე2 · for the…

A:

Q: Find the partial elasticities of z = x'e.

A: Introduction: The partial elasticity of z with respect to x is given by, εx=zxxz The partial…

Q: (ди a?u 0 0 at ax2 u(0,t) = U1, u(x, 0) = f(x), u(L, t) = U2 ,t > 0 0<x<L

A: Please check next steps for the solution.!

Q: x?y" + xy' – y = 16x³, y(1) = 1, y'(1) = 1

A: The solution is given as

Q: (-1)(*+1) + 1 -sin L NAX sinh (nxy/L) 0(x, y) = Σ n sinh (naW/L) n=1 Using this expression,…

A: Given: Temperature distribution equation is as follows: θx,y=2π∑n=1∞-1n+1+1nsinnπxLsinhnπxLsinhnπWL…

Q: Solve the following inhomogeneous heat problem (k = 1): ди d'u Ət Ə.r2 for 0 < x < z with initial…

A: Given: The inhomogeneous heat problem (k = 1): ∂u∂t=∂2u∂x2+cos(x) for 0≤x≤π Initial condition is…

Q: 3. Find the solution of the heat equation 2- = 0 if the boundary conditions are = 0, ôx| = 0 Ix=0…

A: The given heat equation is                       ∂u∂t-2∂2u∂x2=0 ,∂u∂tx=0=0,∂u∂tx=π=0 and ux,0=π2;…