Well I\'m trying to solve second order linear equations using the series method

Question

Well I'm trying to solve second order linear equations using the series method where we have an differential equation in the form of: P(x)y'' + Q(x)y' + R(x)y= 0

My professor said that we should always have all the exponents the same so shift the index until that happens and whenever the index are not the same say all of them are n=0 and one of them are n=1 so I want to change n=1 to n=0 and what my proffesor does is plug in 0 to the n's and if it equals 0 then I can start at n=0 because that change has no effect.

Im concerned when i plug in say 0 for n and it does not equal zero. switching the index to n=0 will change the series but how to include this change into the equation?

Explanation / Answer

you are not actually making n=0 over there,i didnt exactly get your question but you actually take a dummy variable say t=n-1 so when n=1 t will be equal to zero then you can group them.so the series will not get changed.

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