- #1
Husaaved
- 19
- 1
Working through Mathematical Methods in the Physical Sciences by Boas, on the chapter on Series Solutions of Differential Equations, Boas works the example:
[itex] y' = 2xy[/itex]
Boas differentiates the series representation of y yielding y', substitutes both into the original equation, and expands, showing that
[itex] na_n = 2a_{n-2} [/itex]
I see that this is true from expanding each series representation and equating coefficients and so on, but I am having trouble deriving this result from the series notation. Is expansion absolutely necessary to obtain this result, or is there something I'm missing?
[itex] y' = 2xy[/itex]
Boas differentiates the series representation of y yielding y', substitutes both into the original equation, and expands, showing that
[itex] na_n = 2a_{n-2} [/itex]
I see that this is true from expanding each series representation and equating coefficients and so on, but I am having trouble deriving this result from the series notation. Is expansion absolutely necessary to obtain this result, or is there something I'm missing?