Answer 4.1

Write (4.3) as  

We shall solve for T(r) by "separating variables". This technique may be used only when cross-multiplying enables us to put all expressions involving one variable (and its differential) on the left side of the equation and all expressions involving the other variable (and its differential) on the right side, as can be done here. It makes no difference on which sides constants appear. Multiplying both sides of the equation above by dr, we obtain

 
Then from
we have


A and B arbitrary constants.

Then B-A = C is also an arbitrary constant, and we get

(4.4)
where C is an arbitrary constant.

 

Copyright © 1998 Rensselaer Polytechnic Institute. All Rights Reserved.