Taylor Series Method for Solving Second Order Homogeneous Differential Equations

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Among the methods for solving equations of the formwith boundary conditionsandatis the Taylor series method, which uses the original equation to findby repeatedly differentiating atfrom which we can write

Example: Solvegivenandat

(1)

When

Differentiating (1) gives

(2) so when

Differentiating (2) gives

so when

Up to the term inthe solution is

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