Calculus: Verify Thick Walled Cylinder Equations

[Ketav]

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

Homework Equations

How should i go about the solution of this problem

The Attempt at a Solution

I have tried to find solutions for this but get stuck after the substitution of all given info[/B]

 

[Ketav]

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

 

[Chestermiller]

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.

 

[Ketav]

So I've done this,

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