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# Differential Equation: Particular Integral Watch

1. This is the differential equation:

Let the particular integral, s* be:

Hence:

So:

Comparing coeffficients:

But, is:

I know that they are the only variables remaining, but 's is raised to the power of 1, while 's is raised to the power of -1. So, I don't see how they are equal.

Anyways, the pdf I am using for reference tells that the particular integral is:

Which implies that the relationship of C with is true.
2. "Let the particular integral s* be: s*=C\lambda + D"

Wait...are you sure the \lambda s are the same?

EDIT: don't assume I know anything about diffeqs.
3. (Original post by aznkid66)
"Let the particular integral s* be: s*=C\lambda + D"

Wait...are you sure the \lambda s are the same?

EDIT: don't assume I know anything about diffeqs.
It's the trial function for the particular integral.
4. Right, just ignore that.

Yeah, that's weird, it looks a lot like the book is assuming that relationship.

And if s*=mgL/x + L, then:

s*' = -mgL/x^2
s*'' = 2mgL/x^3

Which implies that, after plugging it into the original diffeq:

(2mgL/x^3)+(x/mL)(mgL/x+L)=g+x/m

2mgL/x^3 + g + x/m = g + x/m

Which clearly isn't true when m,g,L,lambda≠0?
5. (Original post by Alpha-Omega)
This is the differential equation:

Let the particular integral, s* be:

Hence:

So:

Comparing coeffficients:

But, is:

I know that they are the only variables remaining, but 's is raised to the power of 1, while 's is raised to the power of -1. So, I don't see how they are equal.

Anyways, the pdf I am using for reference tells that the particular integral is:

Which implies that the relationship of C with is true.
I'm very rusty on these things, and I didn't spot it at first because of the unfamiliar variables (s instead of y and instead of x), but are you sure your DE is the correct one?

The reason I ask is that I've only ever seen a Particular Integral constructed for second order linear DEs and your DE is non-linear because of the presence of the term on the LHS.

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Updated: April 7, 2013
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