- #1
yungman
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[itex] x^2 y'' + x y' + n^2 y = 0 \;[/itex] Is Euler equation and solution is [itex] y=x^m[/itex]
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
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