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I'm starting to learn about differential equation

  1. Jan 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Verify that the differential equation,
    [itex]
    {\frac{dy}{dx}} = 15 - {\frac{2y}{81+3x}}
    [/itex]
    has the general solution
    [itex]
    y(x) = 3(81+3x) + C(81+3x)^{-2/3}
    [/itex]

    2. The attempt at a solution
    I've just learnt about differential equations, so I'm probably missing something very basic. I've tried serperating x and y so that I can integrate and it's not an exact equation.

    Thanks in advance for the help.
     
  2. jcsd
  3. Jan 7, 2013 #2
    Can you differentiate the solution and plug it back into the original differential equation and see if it satisfies the DE?

    -Matt
     
  4. Jan 7, 2013 #3

    CAF123

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    Gold Member

    If you want to solve the differential equation, bring the fractional term on the RHS over to the LHS and you see you have a form that can be solved via integrating factors (the resulting eqn is linear in the independent variable y so this method is valid).
     
  5. Jan 7, 2013 #4

    tiny-tim

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    Science Advisor
    Homework Helper

    hi cambo86! :smile:
    "verify" always means that you don't have to solve it, you just assume the answer, and check it! :wink:

    (by plugging it in, as Matt (leright) :smile: says)
     
  6. Jan 7, 2013 #5
    So I differentiated the general solution and then subsituted that in to the DE. Then I manipulated that to form the general solution again. Is that all that is needed to verify?
     
  7. Jan 7, 2013 #6

    Ray Vickson

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    Science Advisor
    Homework Helper

    I don't understand what you are trying to say. You have a function
    [tex] y = y(x) = 3(81+3x)+C(81+3x)^{−2/3}.[/tex]
    You can compute dy/dx. When you do that, can you re-write dy/dx as
    [tex] 15− \frac{2y}{81+3x}?[/tex]
    If your answer is YES, then you have verified the solution. What other possible meaning could the word "verify" have?
     
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