How to use SERIES to solve DIFFERENTIAL EQUATIONS example: Airy's Equation y''-xy=0

How can we find power series solutions to differential equation? In this video we will see a full example (Airy's equation) of the process. We begin by assuming a series solution to the ODE, substituting it in, shifting the index of the sums to match on both sides, deducing a recurrence relation by comparing the coefficients, and finally solving the recurrence relation to get our final answer.

For the intro video on series solutions, and the rest of the ODE playlist, click HERE: youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9…

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►CALCULUS I: youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ…

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►MULTIVARIABLE CALCULUS III: youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xB…

►DISCRETE MATH: youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxi…

►LINEAR ALGEBRA: youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPN…

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