Show that the following PDE for u(x,y) is linear in u and homogeneous. ди ду ди...
Determine an equilibrium temperature distribution (if one exists) for ди Әt д? и дх2 +x - В for 0 < x < L subject to the boundary conditions ди - (0,t) = 0, дх ди (L, t) = 0, дх and initial condition и(x, 0) = 1. For what values of B are there solutions?
— дt ! [points=4] Q4. Solve the heat equation subject to the given conditions: д?u ди 0<х «п, t> о дх2 ди ди - (0,t) = 0, - (п,t) = 0, t>0 дх дх и(x,0) = п - 3x
i need help with all parts. i will rate.
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Suppose u=f x+y ху is a differentiable function. Which equation must be true? ди ди дхду = 0 од? д?u дх2 ду? + = 0 х2. ди ди - у. дх ду = 0 ди y- дх ди Х- ду = 0 O None of the above Suppose the position vector is given by F(t) = = <t, t², 2) Then at time t = 1, the...
Please help me with this questions, 1a) & 1b).
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ду 1. Find the general solution, u(x,y), of the following PDEs by separation of variables: ди ди (а) 0. ду Ә?и (b) = 0. дудх ди ди (c) tan(x) +y = 0. д ду ие
7. Show that the following functions u(x, y) monic functions v(x, y) and determine f(z) = u(x,y) + iv(x, y) are harmonic, find their conjugate har- as functions of 2. 2x2 2лу — 5х — 22. Зл? — 8ху — Зу? + 2у, (а) и(х, у) (b) и(х, у) (с) и(х, у) (d) u(a, y) 2e cos y 3e" sin y, = 3e-* cos y + 5e-" sin y, = elx cos y - e y sin y, (e) u(x,...
Solve the following partial differential equation by the
variable separation method:
Ә?u Әr2 ди ду +u(x, y)
Solve the heat flow problem: ди ди - (x, t) = 2 — (x, t), 0<x<1, t> 0, д дх2 и(0, t) = (1,1) = 0, t>0, и(x, 0) = 1 +3 cos(x) – 2 cos(3лх), 0<x<1.
Let u = u(x,y) and x = x(r,9), y = y(r,). ди ди a. Let x = r cos Q, y = r sin p. Find and a2u ar' 29 ar2 b. u = -x x = r sin 29,y = r tan’ 4, P (1,5). Find ou at the point P. де до
1. Consider the following system of equations Show that we can solve it uniquely for u and v as functions of r and y near the point (x,y, u, v) - (1,1, i, 1) and find ди/ду, ди/ду at the point (1, 1).
1. Consider the following system of equations Show that we can solve it uniquely for u and v as functions of r and y near the point (x,y, u, v) - (1,1, i, 1) and find ди/ду,...
[points=4] Q4. Solve the heat equation subject to the given conditions: д?u ди О<x<п, to дх? at' ди ди - (0,t) = 0, - (п,t) = 0, t>0 дх дх u(x,0) = п-х Paragraph В І := =