• Support PF! Buy your school textbooks, materials and every day products Here!

Euler's rule or Non-homogenous method?

  • Thread starter lost_math
  • Start date
5
0
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?
 

Answers and Replies

dextercioby
Science Advisor
Homework Helper
Insights Author
12,965
536
U can divide by "x" (assuming x different from 0) and then write the resulting eqn as

[tex] (xy)'=-5x^{4} [/tex]

Integrate both terms and then see what you get.

Daniel.
 
68
0
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...
 
1,073
1
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.
 
68
0
He didn't miss a term, your solution and his are identical, yours is just more detailed.
Right :smile:
 
5
0
Thanks all, was really helpful.
 

Related Threads for: Euler's rule or Non-homogenous method?

  • Last Post
Replies
9
Views
6K
Replies
0
Views
2K
Replies
5
Views
2K
  • Last Post
Replies
1
Views
6K
Replies
2
Views
1K
Top