Notices
Results 1 to 5 of 5

Thread: 2nd Order ODE "Contradiction"?

  1. #1 2nd Order ODE "Contradiction"? 
    Member iopst's Avatar
    Join Date
    Apr 2013
    Posts
    86
    To solve a 2nd order ODE, we can follow the steps as shown below. (Image 2 is a continuation from Image 1, apologies for the size difference.)





    The method to obtain the solution is straightforward.




    Let's say



    If k = -1, a possible solution is y = sin x. If k = 1, a possible solution is y = e^x.


    How do we obtain these two different solutions from one straightforward method?
    "It's not the facts that are important, but the way we think about them."

    - W. Lawrence Bragg
    Reply With Quote  
     

  2. #2  
    Administrator Markus Hanke's Avatar
    Join Date
    Jan 2013
    Location
    Ireland
    Posts
    1,378
    Quote Originally Posted by iopst View Post
    How do we obtain these two different solutions from one straightforward method?
    Remember that this is a differential equation; choosing different values for k gives you completely different equations with completely different solutions, as you have demonstrated with your example. This isn't really surprising.
    Reply With Quote  
     

  3. #3  
    Member iopst's Avatar
    Join Date
    Apr 2013
    Posts
    86
    Quote Originally Posted by Markus Hanke View Post
    Remember that this is a differential equation; choosing different values for k gives you completely different equations with completely different solutions, as you have demonstrated with your example. This isn't really surprising.
    I wasn't surprised, just puzzled.

    How does it all work out mathematically? In terms of getting two different solutions.
    "It's not the facts that are important, but the way we think about them."

    - W. Lawrence Bragg
    Reply With Quote  
     

  4. #4  
    Administrator Markus Hanke's Avatar
    Join Date
    Jan 2013
    Location
    Ireland
    Posts
    1,378
    Quote Originally Posted by iopst View Post
    I wasn't surprised, just puzzled.

    How does it all work out mathematically? In terms of getting two different solutions.
    I am not really sure what you are asking. The presence or absence of the minus sign makes this two completely different equations, hence you get two completely different solutions. Differential equations do not behave the same way as algebraic equations.
    Reply With Quote  
     

  5. #5  
    Member iopst's Avatar
    Join Date
    Apr 2013
    Posts
    86
    Quote Originally Posted by Markus Hanke View Post
    I am not really sure what you are asking. The presence or absence of the minus sign makes this two completely different equations, hence you get two completely different solutions. Differential equations do not behave the same way as algebraic equations.
    Nevermind I've figured it out.
    "It's not the facts that are important, but the way we think about them."

    - W. Lawrence Bragg
    Reply With Quote  
     

Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •