how to solve y=y`/lny`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The request of the problem is vague,hence, supposing that you need to solve `y = (y')/((ln y)') =>`  `y = y*(dy)/(dx),` , you need to perform the following such that:

`y - y*(dy)/(dx) = 0 => y(1 - (dy)/(dx)) = 0 => {(y(x) = 0),(1 - (dy)/(dx)):}`

`1 - (dy)/(dx) = 0 => (dy)/(dx) = 1 => dy = dx`

You need to integrate both sides such that:

`int dy = int dx => y = x + c` , represents a constant

Hence, evaluating the solutions to the equation `y = y*(dy)/(dx)`  yields `y = 0`  and `y = x + c` .

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