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Homework Help: Differential Equations.

  1. Oct 29, 2006 #1
    I missed class last Thursday and I am completely confused about the homework. I tried reading the text but there aren't any example problems like this one. Anyone know any free resources for James Stewart Single Variable Calculus?

    Well here is the question:

    For what values of k does the function y=cos kt satisfy the differential equation 4y"=-25y.
    For those values of k, verify that every member of the family of functions y=A sin kt + B cos Kt.

    I tried solving for y" and setting the equations equal to eachother. To tell the truth I don't understand what the question is saying.

    Thanks for any help!
  2. jcsd
  3. Oct 29, 2006 #2
    Have you tried to solve the equation directly

    y'' = -k^2*cos(kt)
    y = cos(kt)

    than you get two values of k +/-.
  4. Oct 30, 2006 #3


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    Science Advisor

    For a problem where you are asked "show that A is a solution to problem B", actually solving the problem is overkill. Suppose you were asked to show that x= 1 is a solution to the equation x5- 3x4+ 2x3- 4x2+ 3x- 1= 0. Would you solve the equation or just substitute 1 for x and see if the resulting equation is true?

    sristi, substute cos(kt) into 4y"= 5y and see what happens. For what values of k is the resulting equation true?
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