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
Use undetermined coefficients to solve the differential
equation. Linearly independent solutions to the associated
homogeneous ODE are also shown. (please provide a detailed
procedure to understand)
?2?′′ − 4??′ + 6? =
?4e-3x
y1=x2
y2=x3
An object is thrown vertically upward from the ground with an initial velocity of 1960 cm/s. neglecting air resistance, find a) the maximum height reached, and b) the total time is taken to return to the starting point.