Question

Use a power series centered about the ordinary point x0 = 0 to solve the differential equation

(x − 4)y′′ − y′ + 12xy = 0

Find the recurrence relation and at least the first four nonzero
terms of each of the two linearly inde-

pendent solutions (unless the series terminates sooner).

**What is the guaranteed radius of
convergence?**

Answer #1

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.
y′′ + xy = 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
independed sollutions (unless the series terminates sooner). If
possible, find the general term in each solution.
y"+k2x2y=0, x0=0,
k-constant

Series Solution Method. 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′′ + y = 0, x0 = 0

solve y'-y=0 about the point X0=0 by means of a power series.
Find the recurrence relation and two linearly independent
solutions. ( X0 meaning X naught)

Use a series centered at x0=0 to find the general solution of
y"+x^2y'-2y=0. Use a series centered at x0=0 to find the general
solution. Write out at least 4 nonzero terms of each series
corresponding to the two linearly independent solutions.

Find the first four nonzero terms in a power series expansion
about x0 for a general solution to the given
differential equation with the given value for x0.
x2y''-y'+y = 0; x0 = 2

Find a power series solution for the differential equation,
centered at the given ordinary point: (a) (1-x)y" + y = 0, about
x=0
Please explain final solution and how to summarize the recursive
relationship using large pi product (i.e. j=1 to n)

Differential Equation:
Determine two linearly independent power series solutions
centered at x=0.
y” - x^2 y’ - 2xy = 0

find the minimum convergence radius of the solutions on power
series of the differential equation (x^2 -2x+10)y''+xy'-4y=0
surrounding the ordinary point x=1

2. Without actually solving the differential equation (cos x)y''
+ y' + 8y = 0, find the minimum radius of convergence of power
series solutions about the ordinary point x = 0.
and then, Find the minimum radius of convergence of power series
solutions about the ordinary point x = 1.

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