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Math Help - Help with second order initial value problem

  1. #1
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    Help with second order initial value problem

    y''+8y'-9y=0, y(1)=1, y'(1)=0

    I have found that the two roots for this are r_1=-9, r_2=1

    So, y(t)=c_1e^{-9t}+c_2e^t
    y'(t)=-9c_1e^{-9t}+c_2e^t

    After this, I get pretty lost trying to get the correct values for c1 and c2. Can someone help out with this part please? I know that the ans. to this problem is y=1/10e^{9-9t}+9/10e^{-1+t}
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  2. #2
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    Quote Originally Posted by steph3824 View Post
    y''+8y'-9y=0, y(1)=1, y'(1)=0



    So, y(t)=c_1e^{-9t}+c_2e^t
    y'(t)=-9c_1e^{-9t}+c_2e^t
    Use  y(1)=1, y'(1)=0

    So,

    y(1)=c_1e^{-9\times 1}+c_2e^1 = 1

    and

    y'(1)=-9c_1e^{-9\times 1}+c_2e^1= 0

    Now simplify and solve.
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  3. #3
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    Well that's what I'm needing help with is the simplifying. I think that c_2=1-c_1e^{-9}/e but I'm not even positive this is correct, does it become c_2=1-c_1e^{-10}?


    So if the first thing is correct you get -9c_1e^{-9}+(1-c_1e^{-9}/e)e=0 and then -9c_1e^{-9}+1-c_1e^{-9}=0

    I don't really know if that is correct and if it is how do you get c_1? I've forgotten the exponent rules and what not
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  4. #4
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    I get c_2 = \frac{-9c_1}{e^{10}}
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  5. #5
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    Nevermind, after working with the numbers a bit I have figured it out
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