Question

(x^2)*y'' + 5*x*y' - 5y = 0

Answer 1

Im not sure what happens to the x.. do u ignore it when u do r^2 + 5r - 5 = 0 or u do something else?

Answer 2

this is called Cauchy-Euler equation. because of it shapes , it is very easy to solve it

y=t^r
y'= r t^(r-1)
y''= (r(r-1))t^(r-2)

r(r-1) + 5 r -5 =0

r^2 - r+ 5r-5=0

r^2+4r-5=0

(r +5)(r -1)

r=-5,1

Answer 3

Ooooo ok, i remember now thanks!