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Calculus: Verify Thick Walled Cylinder Equations

  1. Nov 8, 2016 #1
    1. The problem statement, all variables and given/known data

    I have a system of two ordinary differential equations as shown below. I have to prove that the Lame's exact solutions for a thick walled cylinder loaded by internal pressure satisfies the equations.

    The next step is to integrate the equations to obtain an equation for U and radial stress

    2. Relevant equations
    How should i go about the solution of this problem

    3. The attempt at a solution
    I have tried to find solutions for this but get stuck after the substitution of all given info
  2. jcsd
  3. Nov 9, 2016 #2
    I have tried to substitute the equations but for the hoop stress I obtain the relationship between b and r as one.
    If anyone has any suggestions, I will be very thankful to you.
    I have tried solving the differential equations however, i get to a point where I get d2u/dr2 + i/r du/dr + u/r=0 and get stuck with integration constants
  4. Nov 11, 2016 #3
    This is really a math problem. I'm going to move it to the math homework forum. Please show us your work in doing the substitutions.
  5. Nov 14, 2016 #4
    So Ive done this,

    now im confused about the integration. its a double integral but the boundary conditions are for r and sigma r

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