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Thread: Rearranging to get a linear differential

  1. #1
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    Rearranging to get a linear differential

    Hi

    I have the following value problem :

    du/dx = xu


    So i rearranged this to become:

    du/dx * 1* 1/u = x

    I there for concluded:
    g(x) = 1 and h(x) = x

    I then did this calculation:



    The book's solutions how ever gives a different answer since it chose different values for g(x) and h(x). I am wondering if mine is still valid or have i done it wrong? Does u have to be u^1 and nothing else for this to work ?

    This is the books solution:

    Rearranging to get a linear differential-capture.jpg
    Rearranging to get a linear differential-capture2.jpg
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  2. #2
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    Re: Rearranging to get a linear differential

    The books answer is correct.

    The form of a first order linear differential equation is

    $u^\prime + g(x)u=h(x)$

    there is no $\dfrac 1 u$ term
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  3. #3
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    Re: Rearranging to get a linear differential

    if a differential equation is not "linear" to begin with, no "rearranging" will make it linear!
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  4. #4
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    Re: Rearranging to get a linear differential

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