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I understand the three cases with different solution. But my question is if n=0.

If I use [itex] y=x^m \;\Rightarrow\; m(m-1)+m=0 \;\Rightarrow m^2 = 0 \;\Rightarrow m=0[/itex]

That would not work. I know the answer is [itex] y=C_1 ln(x) + C_2 [/itex]

Can anyone show me or give me hint how to derive this, I can't find it in my book.

Thanks