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**Linda200** Find two linearly independent solutions of

x^{2}y''+x y'' + y = 0

Also find the solutions which satisfy

y_{1}(1) = 1, y'_{1}(1)=0, y_{2}(1) = 0, y'_{2}(1)=1,

So subbing in y(x)= x^{r }You get solutions y_{1}(x) = x and y_{2}(x)=x^{-1} which are linearly independent,

y_{1} satisfies the solutions provided by y_{2 }does not,

The y_{2} solutions look like they're for ln(x)

Does anyone know how I would get ln(x) as a solutions from x^{-1}? (I know ln(x) is just the integrate of x^{-1} but I don't know why you would integrate)

Thanks

Linda