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!

Determine whether a member of the family can be found that satisfies the boundary conditions.

  1. Sep 22, 2014 #1
    1. The problem statement, all variables and given/known data
    The given two-parameter family is a solution of the indicated differential equation on the interval
    (−infinity, infinity).
    Determine whether a member of the family can be found that satisfies the boundary conditions. (If yes, enter the solution. If an answer does not exist, enter DNE.)

    y = c1e^x cos x + c2e^x sin x; y'' − 2y' + 2y = 0

    I completed the 1st 3 but I dont know this one
    (d) y(0) = 0, y(π) = 0



    2. Relevant equations



    3. The attempt at a solution
    when y(0) = 0 :
    0=c1 e^(0)cos(0)+c2 e^(0)sin(0)
    c1=0

    when y(π) = 0:
    0=c1e^π cosπ+c2 e^π sinπ
    0=c1e^π+0
    c1=0
     
  2. jcsd
  3. Sep 23, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    That tells you that [itex]c_1 = 0[/itex]. But [itex]c_2[/itex] can be anything! You're not asked to find a unique solution, but to find at least one solution.
     
  4. Sep 23, 2014 #3
    so can I say c2=0 making:

    y=e^x cosx ?
     
  5. Sep 23, 2014 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your original problem should have stated you were looking for a solution that isn't identically zero that satisfies the boundary conditions. Your answer I have quoted doesn't satisfy ##y(\pi)=0##. The point is, can you find a ##c_2## that isn't zero so you have a nontrivial solution?
     
  6. Sep 23, 2014 #5

    pasmith

    User Avatar
    Homework Helper

    No, you've already established that the coefficient of [itex]e^x \cos(x)[/itex] must be zero. It's the coefficient of [itex]e^x \sin(x)[/itex] which is arbitrary, since [itex]c_2e^0 \sin(0) = 0 = c_2e^{\pi} \sin(\pi)[/itex] for any [itex]c_2 \in \mathbb{R}[/itex].
     
  7. Sep 23, 2014 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    That is a valid answer but you are taking c2= 1, not 0.
     
  8. Sep 23, 2014 #7

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No it isn't. See post #4.
     
  9. Sep 24, 2014 #8
    can c2 be -cot(x) ? or can I put any number and it will be correct?
     
  10. Sep 24, 2014 #9

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    ##c_1## and ##c_2## are constants. Post #2 pointed out to you ##c_1=0## and ##c_2## can be anything. Try something. Then check if the solution you get satisfies the two boundary conditions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Determine whether a member of the family can be found that satisfies the boundary conditions.
  1. Boundary conditions. (Replies: 4)

  2. Boundary Condition (Replies: 7)

Loading...