Power series method

II-Power series method
We consider the second-order linear homogeneous differential equation for

where ??(??), ??(??) and ??(??) are polynomials. The idea of power series method is to assume that the unknown function can be expanded into a power series:



Substituting in the differential equation and requiring that the coefficients of each power of sum to zero, we can find all the constants in terms of
Example 1:
Solution :

II-Power series method
We consider the second-order linear homogeneous differential equation for

where ??(??), ??(??) and ??(??) are polynomials. The idea of power series method is to assume that the unknown function can be expanded into a power series:



Substituting in the differential equation and requiring that the coefficients of each power of sum to zero, we can find all the constants in terms of
Example 1:
Solution :











Example 2:
Solution :



Now











Solve the differential equations















Example 2:
Solution :



Now











Solve the differential equations