Question

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

Answer #1

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 for the equation y'' − y = x
Provide the recurrence relation for the coefficients and derive
at least 3 non-zero terms of the solution.

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

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+6)y=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

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

Find the first four nonzero terms in a power series expansion
about x=0 for a general solution to the given differential
equation.
(x^2+19)y``+y=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-4)y' - y = 0
y(0) = -1
y'(0) = 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

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)

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