Hi,

I'm studying for my final exam at the moment and i found this question from the past exam paper. but i have no idea how to solve it.

can anyone please please help me!!!

thanks!!!!!!

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- Jun 11th 2008, 07:54 AMpandaHELP!! differential equation and bessels function
Hi,

I'm studying for my final exam at the moment and i found this question from the past exam paper. but i have no idea how to solve it.

can anyone please please help me!!!

thanks!!!!!! - Jun 11th 2008, 08:54 AMCaptainBlack
Make the change of variable $\displaystyle y'=y/x^{\alpha}$ and rewrite the de in terms of $\displaystyle y'$ and $\displaystyle x$. Then put $\displaystyle x'=\beta x^{\gamma}$ and you should find that $\displaystyle x'$ and $\displaystyle y'$ satisfy the Bessel equation of order $\displaystyle n$.

RonL - Jun 11th 2008, 09:49 AMpanda
thanks for the reply

just one more question.

how do you know which variable to use??

for instance, how do you choose the 'change of variable'? - Jun 11th 2008, 10:08 AMCaptainBlack
- Jun 14th 2008, 06:58 AMpanda
using http://www.mathhelpforum.com/math-he...1ef959be-1.gif

i got

(y'x^2 - yxalpha)x^-alpha + yxx^-alpha - (2alphaxy)x^-alpha + beta^2.gemma^2.x^2gamma + alpha^2 -n^2.gemma^2)y = 0

is this right???? and i wasnt sure how to use x'=beta.x^gemma from here. - Jun 14th 2008, 09:35 AMCaptainBlack
You do know that the ' do not denote differentiation here don't you?

Try instead $\displaystyle u(x)=y(x)/x^{\alpha}$ first, from this compute $\displaystyle \frac{dy}{dx}$ and $\displaystyle \frac{d^2y}{dx^2}$ in terms of $\displaystyle x$, $\displaystyle u$, $\displaystyle \frac{du}{dx}$ and $\displaystyle \frac{d^2u}{dx^2}$ and substitute into the DE.

RonL