Question

nd a power series solution ? = ∑∞ ?=0 ?_{k}?^{k}
for the particular solution ??(?) defined by the

following differential equation:

?[??(?)]

?? - √(?′1)2 + (?′2)2 = 0

where ?1 = acos(?) and?2 = ????(?) with ? > ? > 1

Answer #1

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 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

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

Solve the following differential equation by assuming the
solution is a power series ?(?) = ∑ ??? ∞ ? ?=0 . Be sure to
clearly indicate the recursion relationship. Simplify as much as
possible. ? ′′ (?) + 9??(?) = 0

Solve the differential equation y"(x)+9xy(x)=0 by assuming the
solution is a power series. Be sure to clearly indicate the
recursion relationship

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

differential equations!!
y'' +y' +2xy= 0 ,what is the solution for the
differential equation's Power series around the point x0 =
0

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-2)y'+y=0

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