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my problem is as follows:

[tex](x − 1)y" − xy' + y = 0 , x > 1 ; y_1(x) = e^x[/tex]

solving this type of diff. eq. says to use [tex]y=y_1(x)V(x)[/tex] which gives me [tex]y=Ve^x[/tex] differentiating y gives me

[tex]y'=V'e^x[/tex] &

[tex]y''=V''e^x[/tex]

when pluged into original equation i have

[tex](x-1)e^xV''-xe^xV'=0[/tex] with substitution [tex] V'=u[/tex]

from this point on i am not sure whether i should omit (x-1) since x>1 and cannot be zero, or should i include it. But no matter which road i take, i get a solution that includes some combination of e

^{x}. book gives me solution as

**x**, which, upon check is the right solution.. help how to get there is appreciated !