Simple looking 1st order ode

  • #1
Hello people

I am an engineer and therefore not a great mathematician.

To solve a problem involving laminar flow i need to solve the equation with a general form

dp/dx + A/p - B = 0 which I don't know how to do.

Can anyone shed any light on how to solve this simple looking problem.

Many thanks

Jerome
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,306
48
For B = 0 the solution can be written as
[tex]p^2 = - 2 A x + c[/tex]

For B not equal to 0, Mathematica gives something with a ProductLog, so there is probably no nice solution, except for special values of A and B.
 
  • #3
55
0
Seperation of variables gives you the implicit solution

p+(A/B)ln(Bp-A)=Bx + constant.
 
  • #4
Dear Defunc

Many thanks for your reply. I'd be very grateful if you could explain to me how you got the solution. I could not see how to separate variables because of the constant term B.

Many thanks

Jerome
 
  • #5
55
0
You can seperate it to obtain te following:


p/(Bp-A) dp=dx.
 
  • #6
thanks, that has helped me a lot!!!
 

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