- #1

madcattle

- 10

- 0

## Homework Statement

Hey all, this is my first time posting here. I've used your help before, but have not actually ever had to post a question. Thanks for any help you can give, I am excited to finally join the community.

I am doing calculus homework and I am having trouble solving this problem using the Cauchy-Euler method that we're supposed to solve it with.

Solve: xy

^{4}+ 6y

^{m}= 0

It is the part about the 6y

^{m}that I am not sure what to do with.

## Homework Equations

a

_{n}d

^{n}y / dx

^{n}...a

_{0}y = 0

## The Attempt at a Solution

My book toldme to try and substitute y=x

^{m}into the derivative parts, and all of the other problems I've done work with that method. This is what I've done so far.

y=x

^{m}

y

^{1}=mx

^{m-1}

y

^{2}=m(m-1)x

^{m-2}

y

^{3}=m(m-1)(m-2)x

^{m-3}

y

^{4}=m(m-1)(m-2)(m-3)x

^{m-4}

I know how to treat the 4th derivative term; again, I just don't know what or how to think about the y^m term. I know the solution to the problem, as it is in the back of my book, I just don't know how to get there. Can anyone give me a prod in the right direction?

Thanks