Question

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)

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 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

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?

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

Solve by using power series: y'=
(x7) (y) . Find the recurrence
relation and compute the first 33 coefficients.
this is NOT y' = x7y. NOT that.

Solve by using power series: 2y'−y = e^x . Find the recurrence
relation and compute the first 6 coefficients ( ) a0 − a5 .

Solve by using power series: y' =
x^5(y). Find the recurrence relation and compute the first 25
coefficients. Check your solution to the differential equation with
the original equation if possible, please.

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.

Use the power series method to obtain power series solutions
about the given point.
a. y′ = y−x, y(0) = 2, x0 = 0.
b. (1+x)y′(x) = py(x), x0 = 0.

Solve by using power series:
y"+3y'+y=sinh(x)
. Find the recurrence relation and compute the first 6 coefficients
(a1-a5). Use the methods of chapter 3 to solve the differential
equation and show your chapter 8 solution is equivalent to your
chapter 3 solution.

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