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Calculus: Verify Thick Walled Cylinder Equations

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1. Homework Statement

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

upload_2016-11-8_17-15-31.png

2. Homework 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
 
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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
 
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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
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.
 
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So Ive done this,

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



upload_2016-11-15_1-0-33.png
 

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