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theEric

  • 2 years ago

Hi! I am solving a problem, and I think I correctly arrived at \(\ln\left|e^y-2x\ y\right|=C\). At any rate, I think I'll be left with \(\ln\left|e^y-2x\ y\right|\), and I don't know how to solve for \(y\)!

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  1. theEric
    • 2 years ago
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    What I have done is this:

  2. theEric
    • 2 years ago
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    Put each side as the exponent of \(e\). Then \(e^{\ln\left|e^y-2x\ y\right|}=e^C\\\implies e^y-2x\ y=C\) where \(C\) is still just an arbitrary constant.

  3. myko
    • 2 years ago
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    Let me guess, you solving a ODE? Not always it is posible to explicitly express y as function of x. Sometimes you just leave a general solution in implicit form

  4. theEric
    • 2 years ago
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    This is from an ODE.... I am supposed to solve it implicitly. Have I done that, then?

  5. theEric
    • 2 years ago
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    Assuming I got there correctly, I mean. I don't want to ask you to check my work.

  6. myko
    • 2 years ago
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    yes, you are done

  7. theEric
    • 2 years ago
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    Thank you! :)

  8. myko
    • 2 years ago
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    yw

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