# Euler's rule or Non-homogenous method?

1. Homework Statement
x^2 y' + xy + 5x^5=0

2. Homework 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?

Related Calculus and Beyond Homework Help News on Phys.org
dextercioby
Homework Helper
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.

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...

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

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