[tex] x^2 y''+2xy'-12y=0,y_1=x^3 [/tex]
[tex] y''+(2y')/x-12y/x^2 =0 [/tex]
The Attempt at a Solution
[tex] y=uy_1=ux y'=u' x+u y''=u'' x+2u' [/tex]
subbing that in instead of y,y',y''
[tex] u'' x+2u'+2(u'x+u)/x+12(ux)/x^2 =0 [/tex]
now my book says to reduce the order v=u' which is easy enough except for the fact that I have "u" in there with no derivative. What do I sub here (integral of v)????? STUMPED!
thanks for any help