(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am studying for the exams, and not terribly practiced on DE's yet. From a mock-test I found this DE - it be solved? A complete solution would be appreciated so I can understand the answer and compare it to my notes please...

dy/dx - 2xy = ( y ln (y) ) / x

3. The attempt at a solution

I have attempted so far:

a) Separate variables.

I cannot, I get stuck at something like dy + ( -2XY -(Y ln(y)) ) dx = 0, which I tried to make dy*x/y + (-2x^2 -lny )dx = 0 and cannot find a way to separate further

b) Find a multiplicator (is it how is it called? sorry I am not a native English speaker and not yet very familiar with English mathematics terminology), anyway, something to multiply it with so that it can become directly differentable. I don't know how to go about it at the moment.

c) Find a suitable transformation. No luck...

Thanks for reading, thanks for the solution if you provide it...

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# Differential Equation - should be simple, but?

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