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Math Help - Second order homogenous DE - Tricky

  1. #1
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    Second order homogenous DE - Tricky

    I started by trying to find the auxillary equation, as this is a homogenous second order DE.

    I get to this:

    k^2 - 2k + 1 + E^2


    What can I do from here? (k-1)(k-1) + E^2 ???
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  2. #2
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    Quote Originally Posted by chr91 View Post
    I started by trying to find the auxillary equation, as this is a homogenous second order DE.

    I get to this:

    k^2 - 2k + 1 + E^2


    What can I do from here? (k-1)(k-1) + E^2 ???
    For part a you are on the right path

    \displaystyle (k+1)^2+\epsilon^2=0 \implies k+1=\pm i\epsilon \iff k = -1\pm i\epsilon

    Now write down the solution and see what happens as \epsilon \to 0

    For part b put the equation in standard form and solve. Then take the limits
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    For part a you are on the right path

    \displaystyle (k+1)^2+\epsilon^2=0 \implies k+1=\pm i\epsilon \iff k = -1\pm i\epsilon

    Now write down the solution and see what happens as \epsilon \to 0

    For part b put the equation in standard form and solve. Then take the limits
    Thanks, so for a, the complementary function is y = e^x (A cos E x + B sin E x)

    But I'm finding it hard to find the values for A and B to find the general solution.

    For example y = e^x (A cos E x + B sin E x) and x=0, y=1

    1 = 1(AcosE)

    So A = 1/cosE ?


    EDIT : it's k = 1+or- E
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