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Math Help - Problem with a Diff Equation

  1. #1
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    Problem with a Diff Equation

    I am having problems solving this differential equation:

    (dy/dx) = (x + y)^2

    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by machi4velli View Post
    I am having problems solving this differential equation:

    (dy/dx) = (x + y)^2

    Any help would be appreciated.
    We have,
    y'=(x+y)^2
    Define a new function,
    z=x+y.
    Then,
    z'=1+y'\to y'=z'-1
    Thus,
    z'-1=z^2
    z'=1+z^2
    \frac{z'}{1+z^2}=1
    \int \frac{z'}{1+z^2} dx=\int 1 dx
    \tan^{-1} z=x+C
    \tan^{-1} (x+y)=x+C
    Are all the solutions on some non-zero open interval.
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