I'm reading up on some methods to solve differential equations. My textbook states the following:(adsbygoogle = window.adsbygoogle || []).push({});

"[itex]y_{1}[/itex] and [itex]y_{2}[/itex] are linearly independent ... since [itex]\sigma_{1}-\sigma_2[/itex] is not an integer."

Where [itex]y_{1}[/itex] and [itex]y_{2}[/itex] are the standard Frobenius series and [itex]\sigma_1[/itex] and [itex]\sigma_2[/itex] are the roots of the indicial equation.

I'm having trouble seeing how the above follows and would appreciate some input. I'm using "Essential Mathematical Methods for the Physical Sciences" and the quote is (albeit slightly paraphrased) from page 282, for reference.

Incidentally this is my first post. Looking forward to participating in this forum.

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# Frobenius Method - Roots differ by integer

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