Euler Equation -- diff. equations hw

[Arij]

Homework Statement

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Consider the differential equation (t-2)²y"-2(t-2)y'+2y=0, t>2

Find r+,r-roots of the indicial polynomial of the equation above.

Homework Equations

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The Attempt at a Solution

y'-[2/(t-2)]y'+[2/(t-2)^2]y=0

but then I am confused on how to set p(r), what do I do with the t in my a₁ and a₀thanks in advance :)

 

[LCKurtz]

I think that if, instead of trying to plug in numbers in formulas, you try plugging in a solution of the form $y=(t-2)^r$ and see what happens you will answer your own question.

 

[Arij]

I think that if, instead of trying to plug in numbers in formulas, you try plugging in a solution of the form $y=(t-2)^r$ and see what happens you will answer your own question.

oh wow, that's brilliant! it worked! but can you explain more on why you chose this approach?

thank you

 

[LCKurtz]

oh wow, that's brilliant! it worked! but can you explain more on why you chose this approach?

thank you

If you look in your text where they derive the indicial equation, I bet you will find that a substitution like that is where the indicial equation comes from. This is an example where it is much better to understand the method than to memorize the resulting formula.

 

[Arij]

If you look in your text where they derive the indicial equation, I bet you will find that a substitution like that is where the indicial equation comes from. This is an example where it is much better to understand the method than to memorize the resulting formula.

Ops my bad. it's just that we were not required to get a textbook for the class and I was only referring to my notes.
is there any book you recommend?

 

[LCKurtz]

Ops my bad. it's just that we were not required to get a textbook for the class and I was only referring to my notes.
is there any book you recommend?

There are lots of online notes about it. One such is
http://math.arizona.edu/~rjenkins/files/422/hw6soln.pdf