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Math Help - first order non-linear equation

  1. #1
    Junior Member
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    first order non-linear equation

    hi all,

    i have the following question puzzling me:

    (dy/dx) = 10^(x+y)

    how do i solve it?
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  2. #2
    Senior Member
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    Re: first order non-linear equation

    Quote Originally Posted by vonflex1 View Post
    hi all,

    i have the following question puzzling me:

    (dy/dx) = 10^(x+y)

    how do i solve it?
    Notice that \int 10^{-y}dy=\int 10^xdx.
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  3. #3
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    Re: first order non-linear equation

    Hello,

    Maybe, you can use, that
    10^{-y} = e^{-y \ln 10}~.



    Then you get the simple ODE:

    \frac{d}{dx} \left( -\frac{1}{\ln 10} 10^{-y} \right) = 10^x~.
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  4. #4
    MHF Contributor

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    Re: first order non-linear equation

    Of course, the first step, which then leads to what hatsoff and Chandler26 said, is to recognize that 10^{x+y}= 10^x10^y.
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