find_the_fun
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I'm trying to solve [math]a(x-x_0)y''+b(x-x_0)y'+cy-c=0[/math]
So I let $$y=(x-x_0)^m$$ then $$y'=m(x-x_0)^{m-1}$$ and $$y''=m(m-1)(x-x_0)^{m-2}$$
plugging in gives [math]a(x-x_0)m(m-1)(x-x_0)^{m-2}+b(x-x_0)m(x-x_0)^{m-1}+c((x-x_0)^m-1)=0[/math]
now I want to find the values of m that make the equation 0, but factoring seems to be an impossible task?
So I let $$y=(x-x_0)^m$$ then $$y'=m(x-x_0)^{m-1}$$ and $$y''=m(m-1)(x-x_0)^{m-2}$$
plugging in gives [math]a(x-x_0)m(m-1)(x-x_0)^{m-2}+b(x-x_0)m(x-x_0)^{m-1}+c((x-x_0)^m-1)=0[/math]
now I want to find the values of m that make the equation 0, but factoring seems to be an impossible task?