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ubhik · #1 April 30th, 2008, 01:26 PM

I have the following equation in my notes and need to follow it to do another question, can someone tell me how the following line:

$(Ly)=(\frac{d^2}{dx^2}-\frac{2}{x}\frac{d}{dx}+\frac{2}{x^2})y(x)=xln(x)=h(x)$

The kernel of $L$ is found by solving $Ly = 0$

This form suggests trying $y = x^m$ . Substituting,

(I don't understand how the following line is obtained???

)

$L(x^m) = [m(m-1)-2m+2]x^{m-2}= 0$

How does m turn into the base?

I know that:

$y=x^m$

$\frac{dy}{dx}=mx^{m-1}$

and

$\frac{d^2y}{dx^2}=m(m-1)x^{m-2}$

but I still don't understand, how the previous bit is obtained!