Express solution as bessel function

Kazz81
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Hi Guys, I'm an undergrad student...and i have a difficulty trying to solve

4xy" + 4y' + y = 0, and express the solution in term of Bessel function.

I have tried Frobenius method...then...it didn't work..and I'm really confused

Could anyone please help me with this?...i'd would really appreciate!
 
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Bessel fuinctions are defined as solutions to Bessel's equation.

What is Bessel's equation?

Can you, perhaps by changing varables, change your equation to Bessel's equation?
 
Even if I multiply x thru, then divide 4 thru...i still don't get (x^2)y...hmmm..(i.e. Bessel eqn order of zero)..
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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