I have a problem with differential equations - 2nd order - reduction of order(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: 2nd order Differential Eq. - Reduction of Order

**Physics Forums | Science Articles, Homework Help, Discussion**