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Math Help - Constant coefficients initial value problem

  1. #1
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    Constant coefficients initial value problem

    y" -4y' + 3y = 0 y(0)= -1 ; y'(0)= 3

    Here's how I tried to solve it:
    1. r^2 - 4r + 3 = 0
    2. (r-1)(r-3) = 0
    3. r= 1, 3
    4. Thus y=c1(e^x) + c2(e^3x)

    But now I'm stuck. How do I use the initial values to solve for c1, c2?

    Thanks,

    Jim
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by Jim Newt View Post
    y" -4y' + 3y = 0 y(0)= -1 ; y'(0)= 3

    Here's how I tried to solve it:
    1. r^2 - 4r + 3 = 0
    2. (r-1)(r-3) = 0
    3. r= 1, 3
    4. Thus y=c1(e^x) + c2(e^3x)

    But now I'm stuck. How do I use the initial values to solve for c1, c2?

    Thanks,

    Jim
    y\Rightarrow f(x)=c_1e^x + c_2e^{3x}

    -1 \Rightarrow f(0) = c_1 + c_2

    f'(x)=c_1e^x + 3c_2e^{3x}

    3 \Rightarrow f'(0) = c_1 + 3c_2

    You now have a system of equations like so:

    c_1 + 3c_2 = 3
    c_1 + c_2 = -1

    I'm sure you can finish this!
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