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 November 7th, 2017, 02:29 AM #1 Senior Member   Joined: Nov 2011 Posts: 250 Thanks: 3 Implict function Is problem of mathematic of Implict function that impossible to solve? and my next question: Is there problem that hard to solve but solvable in Implict function subject? And the last question (connected to the others): Is there hardest question in this subject? Thank for answering me, You are welcome.
November 7th, 2017, 07:32 AM   #2
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Quote:
 Originally Posted by shaharhada Is problem of mathematic of Implict function that impossible to solve? and my next question: Is there problem that hard to solve but solvable in Implict function subject? And the last question (connected to the others): Is there hardest question in this subject? Thank for answering me, You are welcome.
If you mean "closed form solution" then the answer is "yes" you can write an implicit equation that cannot be solved exactly. It's merely a variation on equations in one variable that cannot be solved. For example: $\displaystyle x^2y + e^{y} = 2$ cannot be solved for y(x). However unless you have an exceptional equation to work with you can usually get an approximate solution.

-Dan

 November 7th, 2017, 07:38 AM #3 Senior Member   Joined: Nov 2011 Posts: 250 Thanks: 3 thanks Why is it hard to solve your exaution? Thank you very much!!!
November 7th, 2017, 08:40 AM   #4
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Quote:
 Originally Posted by shaharhada Why is it hard to solve your exaution? Thank you very much!!!
This is a classic case of an unsolvable equation. Here is a link to its definition. The Lambert function W cannot be solved exactly... you can only approximate a solution. In your case you can't separate the y from the exponential without ending up with a term $\displaystyle \ln( x^2y )$, which is just as bad as the original.

-Dan

Last edited by topsquark; November 7th, 2017 at 08:43 AM.

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