Subject is differential equations.
Find the first four nonzero terms in a power series expansion
about x=0 for a general solution to the given differential
equations.
a) y' + (x+5)y = 0
b) y'' + (x+5)y' + y = 0
c) y'' + 4xy' - y = 0; y(0) = 8, y'(0) = 0
d) y'' + (x-6)y' - y = 0; y(0) = -5, y'(0) = 0
Please show work! Thank you
Series Solutions of Ordinary Differential Equations For the
following problems solve the given differential equation by means
of a power series about the given point x0. Find the recurrence
relation; also find the first four terms in each of two linearly
independent solutions (unless the series terminates sooner). If
possible, find the general term in each solution.
(1-x)y"+xy-y=0, x0=0
Series Solutions of Ordinary Differential Equations For the
following problems solve the given differential equation by means
of a power series about the given point x0. Find the recurrence
relation; also find the first four terms in each of two linearly
independent solutions (unless the series terminates sooner). If
possible, find the general term in each solution.
(4-x2)y"+2y=0, x0