Find the power series in x-xo?

Math10
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Homework Statement


Find the power series in x-x0 for the general solution of y"-y=0; x0=3.

Homework Equations


None.

The Attempt at a Solution


I'll post my work by uploading it.
 
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This is my work.
 

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And the answer is
 

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Math10 said:

Homework Statement


Find the power series in x-x0 for the general solution of y"-y=0; x0=3.

Homework Equations


None.

The Attempt at a Solution


I'll post my work by uploading it.

Don't bother; most helpers will not read it. If you want help the safest way is to type out the solution, which is the PF standard, anyway.
 

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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