How to solve a second order linear homeogeneous ODE with Frobenius?

fabsuk
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A simple question i think although i can't find in any books

What do u when u are solving a second order linear hoemoeneous differential equation with frobenius and there is no shift.

(X^2)(y^{''}) (-6y)=0 it should be normal minus -6y

I only know what to do if there is a shift.Help someone?

This is otherwise known as series solutions to differential equations
 
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Does anybody know?

I keep trying but get nowhere i get an answer of 0 which i wrong.Help
 
Well i think i figured it out.
There is no recurrence relation and so your indical relations become your 2 values of the series.Thanks for the help.:rolleyes:
 

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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