- #1

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" find two linearly independent of frebenius series solutions for 4xy''+2y'+y=0"

I try almost everything to slove this, but could't figure it

any help is appercaited

thank you

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In summary, the question is asking for help on finding two linearly independent solutions for 4xy+2y=0. The user has tried almost everything but has not been successful. They need to assume a solution and find the derivatives. Once they have the derivatives, they can substitute them into the equation and solve for y' and y".f

- #1

- 10

- 0

" find two linearly independent of frebenius series solutions for 4xy''+2y'+y=0"

I try almost everything to slove this, but could't figure it

any help is appercaited

thank you

- #2

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Well, what have you done on it? You say you've tried "almost everything". Okay, **what** have you tried?

- #3

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Well, what have you done on it? You say you've tried "almost everything". Okay,whathave you tried?

well, i divided the whole thing by 4x, trying to get it to the general format, but it didnt work out.

- #4

Science Advisor

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Start by writing

[tex]y= \sum_{n=0}^\infty a_n x^{n+c}[/tex]

Find y' and y" from that and put them into the equation. What do you get?

- #5

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Start by writing

[tex]y= \sum_{n=0}^\infty a_n x^{n+c}[/tex]

Find y' and y" from that and put them into the equation. What do you get?

i don't know how to find y' and y''

im slef learning def.Q

thanks for the reply tho.

- #6

- 10

- 0

Start by writing

[tex]y= \sum_{n=0}^\infty a_n x^{n+c}[/tex]

Find y' and y" from that and put them into the equation. What do you get?

by the way, i don't think y' and y'' is needed here

i divided the whole thing by 4x, then slove for the indicial,

which are r=0,-.5

but i don't know what to do from this point on,

i think i need to find the equation for cn, but don't know how.

can you help

- #7

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You don't need to divide by 4x.

When you assume the solution you will find d second and first derivatives of y, you will then subtitute into the equation.

I solved it and that's the way it goes.

- #8

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- #9

Science Advisor

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It's probably not a good idea to try to learn differential equations, by your self or not, if you do not know Calculus!i don't know how to find y' and y''

im slef learning def.Q

thanks for the reply tho.

Are you seriously saying that you do not know how to find the derivatives of x

And, to even attempt a problem like this you should have had enough Calculus to know that a power series is "term by term" differentiable inside its radius of convergence.

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