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Math Help - Differential Equations...

  1. #1
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    Differential Equations...

    a) Write down the general solution of the differential equation dy/dx + 3y = 0.

    b) Use a suitable trial function to find one simple particular solution of dy/dx + 3y = -6

    c) Find the solution of dy/dx + 3y = -6 that satisfies y(0) = -5

    Any ideas?
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  2. #2
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    Quote Originally Posted by mr_motivator View Post
    a) Write down the general solution of the differential equation dy/dx + 3y = 0.

    b) Use a suitable trial function to find one simple particular solution of dy/dx + 3y = -6

    c) Find the solution of dy/dx + 3y = -6 that satisfies y(0) = -5

    Any ideas?
    a) This is first order linear. What do your notes say to do?

    b) Try a solution of the form y = k. What value do you find k has to have?

    c) y = Solution to a) + solution to b). Now substitute x = 0 and y = -5 to solve for the arbitrary constant.
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    Quote Originally Posted by mr_motivator View Post
    a) Write down the general solution of the differential equation dy/dx + 3y = 0.
    Multiply by e^{3x} to get e^{3x}y' + 3e^{3x}y = 0 \implies \left( e^{3x}y \right)' = 0
    Therefore, e^{3x}y = k \implies y = ke^{-3x},k\in \mathbb{R}.
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  4. #4
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    so the answer to a), the general solution to the differential equation is y(x) = kexp(-3x) ?

    Or is this the answer to b), the trial function? If anyone knows a good tutorial for the use of trial functions in this context it would be appreciated as i cannot seem to find any.
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  5. #5
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    Quote Originally Posted by Muzza8888 View Post
    so the answer to a), the general solution to the differential equation is y(x) = kexp(-3x) ?

    Or is this the answer to b), the trial function? If anyone knows a good tutorial for the use of trial functions in this context it would be appreciated as i cannot seem to find any.
    For (b) just take y=-2.
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