Question

Find the power series solution of the differential equation y"-xy'+6y=0 about the ordinary point x=0

Answer #1

Find two solutions of a power series for the differential
equation y'' - xy = 0 surrounding the ordinary point x=0

Let y=2−3x+∑n=2∞an x power n be the power series solution of the differential equation:
y″+6xy′+6y=0 about x=0. Find a4.

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)

1. Find the general solution to the differential equation y''+
xy' + x^2 y = 0 using power series techniques

Power series
Find the particular solution of the differential equation:
(x^2+1)y"+xy'-4y=0 given the boundary conditions x=0, y=1 and y'=1.
Use only the 7th degree term of the solution. Solve for y at x=2.
Write your answer in whole number.

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

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?

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.

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

Find at least one solution about the singular point x = 0 using
the power series method. Determine the second solution using the
method of reduction of order.
xy′′ + (1−x)y′ − y = 0

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