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Math Help - Urgent: ......differential equation (another).

  1. #1
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    Exclamation Urgent: ......differential equation (another).

    Hi it's me again.

    I have another couple of problems I need to solve. (Same as before I have no idea what I am doing, so as much detail as you are willing to give, will be greatly appreciated).

    (Problem 1) Find the general solution of:

    d^2/dx^2 - 4 dy/dx + 5y = 0


    (Problem 2) Find the particular solution of:

    d^2y/dx^2 - y = e^2x , y(0)=0, y'(0)=1,


    Any assistance will be greatly appreciated!!!

    Thank you math_Newbie.
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  2. #2
    Eater of Worlds
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    Let's use Laplace.

    y''-y=e^{2x}, \;\ y(0)=0, \;\ y'(0)=1

    p^{2}Y-py(0)-y'(0)-Y=\frac{1}{p-2}

    Sub in the IC's:

    p^{2}Y-1-Y=\frac{1}{p-2}

    and solve for Y and you get:

    Y=\frac{1}{(p-2)(p+1)}

    Now, find the inverse Laplace of this and we see that we get:

    y=\frac{e^{2t}-e^{-t}}{3}
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  3. #3
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    Exclamation

    Thank you for the pointers, though I am still a little unsure

    Does anyone have any ideas about the first problem?

    (Problem 1) Find the general solution of:

    d^2/dx^2 - 4 dy/dx + 5y = 0


    Your help will be appreciated!!!

    Thank you math_Newbie.
    Follow Math Help Forum on Facebook and Google+

  4. #4
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    Quote Originally Posted by math_Newbie View Post
    Thank you for the pointers, though I am still a little unsure

    Does anyone have any ideas about the first problem?

    (Problem 1) Find the general solution of:

    d^2/dx^2 - 4 dy/dx + 5y = 0


    Your help will be appreciated!!!

    Thank you math_Newbie.
    Click me
    Follow Math Help Forum on Facebook and Google+

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