Abstract:
Linear second order ordinary di erential equations with variable coe fcients and
Legendre equation which is second order variable coe cient ODE frequently occurs
in various elds of science and mathematics,physics involving spherical symetry.are
the whole family of di erential equations.In this thesis,we proposed solving this
linear second order ordinary di erential equation of variable coe cient using power
series method.general solution of the problem is obtained and solve some application
problem of legendre equation.
