# Homework Help: Euler's rule or Non-homogenous method?

1. Jan 14, 2007

### lost_math

1. The problem statement, all variables and given/known data
x^2 y' + xy + 5x^5=0

2. Relevant equations
no starting conditions

3. The attempt at a solution
cannot figure out how to do this. Euler's equations methods have no pure x terms, and the non-homogenous methods have some kind of separable thing, where the x terms neatly land up on RHs and y terms on LHS. But what do i do with this? Is it the polynomial expansion or maybe some kind of taylor series?

2. Jan 15, 2007

### dextercioby

U can divide by "x" (assuming x different from 0) and then write the resulting eqn as

$$(xy)'=-5x^{4}$$

Integrate both terms and then see what you get.

Daniel.

3. Jan 15, 2007

### Stevecgz

I think dextercioby missed a term.

Start by putting in the form y' + y*(1/x) = -5x^3

Next, your integrating factor is p = e^[integral(1/x)dx] = e^(lnx) = x

Continue...

4. Jan 15, 2007

### d_leet

He didn't miss a term, your solution and his are identical, yours is just more detailed.

5. Jan 15, 2007

### Stevecgz

Right

6. Jan 15, 2007