Results 1 to 4 of 4

Thread: Help :(

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    19

    Help :(

    Okay.. Can anyone explain me, how to solve this problem:

    $\displaystyle y''+4y'+4=0$.. when $\displaystyle y(0)=2$ and $\displaystyle y'(0)=0$
    Last edited by mr fantastic; Sep 25th 2009 at 05:54 PM. Reason: Made the boundary conditions clearer.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by MissWonder View Post
    Okay.. Can anyone explain me, how to solve this problem:

    $\displaystyle y''+4y'+4=0$.. when $\displaystyle y(0)=2 and y'(0)=0$
    The Characteristic Equation is

    $\displaystyle m^2 + 4m + 4 = 0$

    $\displaystyle (m + 2)^2 = 0$

    $\displaystyle m = -2$.


    Since the solution of the characteristic equation is repeated, the solution will be of the form

    $\displaystyle y(x) = C_1e^{-2x} + C_2xe^{-2x}$.

    We can also see that

    $\displaystyle y'(x) = -2C_1e^{-2x} + C_2e^{-2x} -2C_2xe^{-2x}$.


    Applying the initial conditions gives

    $\displaystyle 2 = C_1 + C_2$ and $\displaystyle 0 = -2C_1 + C_2$.


    Solving the equations simultaneously gives

    $\displaystyle 2 = 3C_1$

    $\displaystyle \frac{2}{3} = C_1$


    $\displaystyle 2 = \frac{2}{3} + C_2$

    $\displaystyle \frac{4}{3} = C_2$.



    Thus $\displaystyle y(x) = \frac{2}{3}e^{-2x} + \frac{4}{3}xe^{-2x}$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    19

    hmm

    Applying the initial conditions gives

    and .

    Where do you get that last part from?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by MissWonder View Post
    Applying the initial conditions gives

    and .

    Where do you get that last part from?
    The reply given was quite clear. Go back and read it carefully. Especially the part where the given initial condition y'(0) = 0 is substituted into the rule for y'.
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum