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Understanding Differential Equations

  1. Feb 18, 2014 #1
    Hello,

    these are the first differential equations i've tried to solve...

    1. The problem statement, all variables and given/known data

    Find the general solution of the following differential equations. In each case if
    y = 2 when x = 1 find y when x = 3.

    [itex]2x \frac{dy}{dx} = 3[/itex]

    2. Relevant equations



    3. The attempt at a solution

    [itex]2x \frac{dy}{dx} = 3[/itex]

    [itex] \frac{dy}{dx} = \frac{3}{2x}[/itex]

    [itex] dy = (\frac{3}{2x}) dx[/itex]

    [itex]\int dy = \int (\frac{3}{2x}) dx[/itex]

    [itex]y = \frac{3}{2}ln|x| + c[/itex]

    Firstly, is this correct and secondly, the question says that when y = 2, x = 1 but ln(1) = 0 so I don't see how this can be true. Or have I just found out that my constant of integration, c = 2?

    Thanks for any help you can give!

    BOAS
     
  2. jcsd
  3. Feb 18, 2014 #2

    PeroK

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    Science Advisor
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    Gold Member

    I think you've just found the value of your constant of integration!

    If you have solved a diff equ, you can always check your answer by diferentiating it and putting it back in the original equation. It's often worth doing if you're not sure.
     
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