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General solution to a second order homogeneous differential equation

  1. Feb 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Find if it is true that the general solution to : y'' - y' = 0, where y(x),
    can be written as : y(x) = c1 cosh(x) + c2 sinh(x), where c1 and c2 are real
    arbitrary constants.

    2. Relevant equations

    differential equation solving

    3. The attempt at a solution

    I just want to know what the h's mean at the end of sin and cos.
  2. jcsd
  3. Feb 2, 2010 #2


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    Science Advisor
    Homework Helper

    The 'h' means hyperbolic. cosh(x)=(e^x+e^(-x))/2. sinh(x)=(e^x-e^(-x))/2. That's all, it's just an abbreviation for those expressions. Can you show they both satisfy your differential equation?
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