# How do you use Power Series to solve the differential equation #y'-y=0# ?

The solution is

Let us look at some details.

by combining the summations,

so, we have

Let us observe the first few terms.

Hence, the solution is

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To solve the differential equation (y' - y = 0) using power series, you assume a power series solution of the form (y(x) = \sum_{n=0}^{\infty} a_nx^n). Substitute this series into the differential equation, equate coefficients of like powers of (x), and solve for the coefficients (a_n). Then, express the solution in terms of the coefficients.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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