Recent content by walter9459

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    PDE Separation of variables

    Sorry to be so dense, but I get lost at this point. I think I am then suppose to do ut=X(x)[-C(∏/2 + 2m∏)sin(∏/2 + 2m∏)t + D(∏/2 + 2m∏)cos(∏/2 + 2m∏)t) ut(x,0) = D(∏/2 + 2m∏)cos(∏/2 + 2m∏) = x(1-x) ----> D ≠ 0 t = 0 f(x) = ∑ Dsin (∏/2 + 2m∏)t u(x,t) = ∑ D sin ((∏/2 + 2m∏)t sin...
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    PDE Separation of variables

    Homework Statement Solve the problem. utt = uxx 0 < x < 1, t > 0 u(x,0) = x, ut(x,0) = x(1-x), u(0,t) = 0, u(1,t) = 1 Homework Equations The Attempt at a Solution Here is what I have so far but I'm not sure if I am on the right path or not. u(x,t) = X(x)T(t)...
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    PDE Wave Equation/boundary condition question

    Homework Statement I need to visualize the wave equation with the following initial conditions: u(x,0) = -4 + x 4<= x <= 5 6 - x 5 <= x <= 6 0 elsewhere du/dt(x,0) = 0 subject to the following boundary conditions: u|x=0 = 0 Homework Equations I'm not sure I understand the...
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    PDE - Need help getting started.

    Thank you for your patience and help in explaining this in a manner that I was able to understand.
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    PDE - Need help getting started.

    Okay now I have the following: F = ma F = EA(x)U(x) = d/dx[EA(x)d/dx)] = m(x) d^2u/dt^2 u(x,t) = U(x)T(t) d/dx[EA(x) d/dx[U(x)T(t)]] = d^2/dt^2 [m(x)T(t)] t(t) d/dx [EA(x) d/dx [U(x)T(t)] = 1/T(t) d^2/dt^2 T(t) = -w^2 d/dx[EA(x) d/dx U(x)] + w^2m(x)U(x) = 0 I need to get to 1/x^2 d/dx[x^2...
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    PDE - Need help getting started.

    Homework Statement Derive the differential equation governing the longitudinal vibration of a thin cone which has uniform density p, show that it is 1/x/SUP] d/dx(x du/dx) = (1/c) d u/d[SUP]t Hint: The tensile force sigma = E du/dx where E is the Young's modulus (a constant), u is the...
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    PDE Cylindrical and Spherical Symmetry

    okay I have been studying my book all weekend and this is what I had. Laplace Equation (1/r) d/dr(rdu/dr) + (1/r^2)d^2u/ds = 0 (s represents theta) u(r,s)=R(r)S(s) (1/Rr)d/dr(rdR/dr) + (1/(r^2S))(d^2S/ds^2) = 0 (1/S)d^2S/ds^2 = -w^2 and (r/R)d/dr(rdR/dr)= w^2 Therefore S = A cos ws +...
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    PDE Cylindrical and Spherical Symmetry

    Yes I do understand and know the method of Separation of variables.
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    PDE Cylindrical and Spherical Symmetry

    This was all the data I was given. Our book is very brief and assumes you are very proficient with ODE's. I am struggling and need to understand these concepts. Thanks!
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    PDE Cylindrical and Spherical Symmetry

    Homework Statement Show that the solution u(r,theta) of Laplace's equation (nabla^2)*u=0 in the semi-circular region r<a, 0<theta<pi, which vanishes on theta=0 and takes the constant value A on theta=pi and on the curved boundary r=a, is u(r,theta)=(A/pi)[theta + 2*summation ((r/a)^n*((sin...
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    PDE - Fourier Method

    Homework Statement Obtain all solutions of the equation partial ^2 u/partial x^2 - partial u/partial y = u of the form u(x,y)=(A cos alpha x + B sin alphax)f(y) where A, B and alpha are constants. Find a solution of the equation for which u=0 when x=0; u=0 when x = pi, u=x when y=1...
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    Partial Differential Equations Help!

    Sorry to be a pain but I think I am finally getting the idea and want to make sure this is true. ux = f'(2x+y2)*2 + g'(2x-y2)*2 uy = f'(2x+y2)*2y + g'(2x-y2)*-2y uxx = f''(2x+y2)*0 + g''(2x-y2)*0 uyy = f''(2x+y2)*2 + g''(2x-y2)*-2 then I just plug these results into the equation y2uxx +...
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    Partial Differential Equations Help!

    I am still confused, I do not see where the chain rule comes into play, f(x,y) = 2x + y2. So why isn't fx equal to 2? I do not see how you are coming up with (2x + y2)*2. I desperately need to understand this whole concept! Thanks!
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    Partial Differential Equations Help!

    Homework Statement Show that u=f(2x+y^2)+g(2x-y^2) satisfies the equation y^2 d^2u/dx^2 + (1/y) du/dy - d^2u/dy^2=0 where f and g are arbitrary (twice differentiable) functions. Homework Equations The Attempt at a Solution I came up with fxx=0 fyy=2 gxx=0 gyy= 2. But didn't...
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    Power expansion

    Please accept my apologies. I had been studying all day and had hit a wall. I stepped away and when I came back, it all made sense. Your assistance was greatly appreciated! Thank you for all your help!
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