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Math Help - Separable equations

  1. #1
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    Unhappy Separable equations

    Hi!

    I have problem solving this equation

    dy/dx = y/2x

    The answer should be y^2 = Cx

    I cannot understand why you multiply the constant with x...
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  2. #2
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    Quote Originally Posted by Fredrik373 View Post
    Hi!

    I have problem solving this equation

    dy/dx = y/2x

    The answer should be y^2 = Cx

    I cannot understand why you multiply the constant with x...
    \frac{1}{y} \, dy = \frac{1}{2} \int \frac{1}{x} \, dx.

    Therefore \ln |y| = \frac{1}{2} \ln |x| + K = \ln (\sqrt{x}) + K

     \Rightarrow y = \sqrt{x} e^K

    \Rightarrow y^2 = x e^{2K} = C x where C = e^{2K}.
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