1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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: Solving equation simultaneously for constant

  1. Jul 15, 2012 #1
    This is for 2nd order homogenous differential equation but that isn't what needs to be solved. What I need help with is solving simultaneously-- something that I am terrible with.

    With t = 0, y = 2 we have [itex]c_1 + c_2 = 2[/itex]

    Upon differentiation of y, we obtain: [itex]y'=c_1e^t-c_2e^{-t}[/itex]

    With t = 0, y' = -1 [itex]c_1 - c_2 = -1[/itex]

    Now the book says that upon solving these two equations simultaneously, [itex] c_1 = 1/2 & c_2 = 3/2[/itex]

    So I try to verify the result, I set up the two equations to solve by elimination

    [itex]c_1 + c_2 = 2[/itex]
    [itex]c_1 - c_2 = -1[/itex]
    c_2 cancels out & we obtain c_1 = 1 which is the wrong conclusion. I can reason out that c_1 should be 1/2 & c_2 should be 3/2, but first and foremost I want to know why solving by elimination gives the wrong answer and what method would be the correct one.
  2. jcsd
  3. Jul 15, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    [itex]c_1 + c_2 = 2[/itex]
    [itex]c_1 - c_2 = -1[/itex]​
    Then adding the two equations gives
    [itex]2c_1=1\ [/itex]​
  4. Jul 15, 2012 #3
    Oh--duh. That was probably the easiest problem you've had to solve to date :rofl: .

    1 + 1 ≠ 1 .. maybe it is time I get some sleep. :grumpy:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook