Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: First ODE of an absolute value

  1. May 3, 2012 #1
    so I understand the basic premise of differentiating a first ODE, or I thought I did. I have the equation y'-y=abs(x-1). I have no idea of how to go about this. Can someone walk me through how to do this? I'm attempting to study for a test and this is one of the practice questions he gave us so I feel as though I'm in some serious trouble if I don't learn how to do this! Thank you much.
  2. jcsd
  3. May 3, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Can you solve ##y'-y=x-1##? Can you solve ##y'-y=1-x##? These are the two cases you have depending on whether ##x>1## or ##x<1##. Solve them separately.
  4. May 3, 2012 #3


    User Avatar
    Science Advisor

    First, you don't want to "differentiate" the ODE, you want to integrate it.

    And the simplest way to handle the absolute value is to use the definition. If [itex]x\ge 1[/itex], x- 1 is non-negative so |x- 1|= x- 1 and your differential equation becomes dy/dx- y= x- 1.
    If x< 1, x- 1 is negative so|x- 1|= -(x- 1)= 1- x and your differential equation becomes dy/dx= 1- x.

    Integrate those to get two general solutions, one valid for x> 1, the other valid for x< 1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook