Solve M(x,y) from N(x,y) and Equation Provided

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It is not possible to uniquely determine M(x,y) from N(x,y) given the equation N(x,y)^M(x,y) - M(x,y)*e^N(x,y) = 0, as there is one equation with two unknowns. The discussion emphasizes that since M(x,y) depends on both x and y, the lack of additional equations limits the ability to solve for M(x,y). The context is part of a larger differential equation problem. Therefore, without further information or constraints, a unique solution for M(x,y) cannot be achieved.
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Homework Statement



is it possible to find M(x,y) if I know N(x,y) and the equation i need to solve is N(x,y)^M(x,y) - M(x,y)*e^N(x,y) = 0?

both are linear functions

thanks, this is part of a longer differential equation and the above equations is what I end up with. Just need some input please.

Thanks!
 
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If M(x,y) is in terms of both x and y then I would say no, because you only have one equation and two unknowns
 

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