Question

Find a power series solution of the given differential equation. Write the solution in terms of power series of familiar elementary functions.

a. (3? − 1)?′ + 3? = 0

b. ?′ − 10?? = 0

Answer #1

Find the solution of the nonlinear differential equation in
terms of an infinite power series and derive a formula for the
coefficients of the power series expansion for y(x).
y'' - x*y = 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

Consider the differential equation
4x2y′′ − 8x2y′ + (4x2 + 1)y = 0
(a) Verify that x0 = 0 is a regular singular point of the
differential equation and then find one solution as a Frobenius
series centered at x0 = 0. The indicial equation has a single root
with multiplicity two. Therefore the differential equation has only
one Frobenius series solution. Write your solution in terms of
familiar elementary functions.
(b) Use Reduction of Order to find a second...

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)

Find at least the first six non-zero terms of the general power
series solution, centered at the ordinary point ?=0, of the given
differential equation. Write your answer in standard form.
?''−?^2 ?'+?=0

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

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 first four nonzero terms in a power series expansion
about x=0 for a general solution to the given differential
equation.
y'+(x+3)y=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

Find the first four nonzero terms in a power series expansion
about x = 0 for a general solution to the given differential
equation
(x2 + 6)y'' + y = 0

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