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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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 \(y\)!

Calculus1
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What I have done is this:
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.
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

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This is from an ODE.... I am supposed to solve it implicitly. Have I done that, then?
Assuming I got there correctly, I mean. I don't want to ask you to check my work.
yes, you are done
Thank you! :)
yw

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