Solving Euler equationplease check work thanks

[darryw]

Homework Statement

determine the gen sol of the DE

$$x^2y'' - 5xy' + 9y = 0$$


Q/P = A = -5 and R/P = B = 9

then use y = x^r in original DE...
y' = rx^(r-1)
y'' = (r-1)rx^(r-2)

insert into DE
$$x^2 (r-1)rx^{r-2} - 5x(rx^{r-1})+ 9x^r = 0$$

i am confused as to how to proceed.. it looks like a characteristic, but do i separate the x's or what?? please help thanks

 

[tiny-tim]

Hi darryw!

$$x^2 (r-1)rx^{r-2} - 5x(rx^{r-1})+ 9x^r = 0$$

erm … they're all x^r

get some sleep! :zzz:​