- #1

jonneh

- 5

- 0

This is my problem:

Find conditions on [tex]\alpha[/tex] and [tex]\beta[/tex] in the Euler equation x[tex]^{2}[/tex]y'' + [tex]\alpha[/tex]xy' + [tex]\beta[/tex]y = 0 such that:

a) All solutions approach zero as x [tex]\rightarrow[/tex] 0

b) All solutions are bounded as x [tex]\rightarrow[/tex] 0

c) All solutions approach zero as x [tex]\rightarrow\infty[/tex]

I don't really know where to start with this, actually, I have no clue where to start.

Also, what does it really mean for a solution to be bounded? I've been scouring some textbooks for a simple explanation but I can't seem to find it. Does it just mean that the function is constrained to some region?

Any help would be greatly appreciated :D