## Taylor Series Method for Solving Second Order Homogeneous Differential Equations

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