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