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asdf1

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Find a basis of solutions for the following second-order homogeneous linear equation for positive x:

x^2y``-xy`+y=0

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- Thread starter asdf1
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- #1

asdf1

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Find a basis of solutions for the following second-order homogeneous linear equation for positive x:

x^2y``-xy`+y=0

- #2

LeonhardEuler

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Do you know what a Cauchy-Euler equation is?

- #3

HallsofIvy

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What happens if you try a solution of the form y= x

- #4

asdf1

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HallsofIvy said:.

What happens if you try a solution of the form y= x^{r}for some real number r?

- #5

asdf1

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1) for the case of double roots, the proof to the general solution only considers

x>O... why?

2) for the case of complex conjugate roots, there's only a general solution for all

positive x... why?

btw, I've been thinking all day of y=x^r... I'm still stumped over how'd you think of that?

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