Question

Differential Equation:

Determine two linearly independent power series solutions
centered at x=0.

y” - x^2 y’ - 2xy = 0

Answer #1

Series Solutions Near a regular singular point:
Find two linearly independent solutions to the given differential
equation.
3x2y"-2xy'-(2+x2)y=0

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

7. Given that x =0 is a regular singular point of the given
differential equation, show that the indicial roots of the
singularity do not differ by an integer. Use the method of
Frobenius to obtain two linearly independent series solutions about
x = 0. Form the general solution on (0, ∞)
2xy”- y’ + y = 0

Use an appropriate infinite series method about x = 0 to find
two solutions of the given differential equation. (Enter the first
four nonzero terms for each linearly independent solution, if there
are fewer than four nonzero terms then enter all terms. Some
beginning terms have been provided for you.)
y'' − 2xy' − y = 0

Solve the following differential equation using taylor series
centered at x=0:
(2+x^2)y''-xy'+4y = 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

The indicated functions are known linearly independent solutions
of the associated homogeneous differential equation on (0, ∞). Find
the general solution of the given nonhomogeneous equation.
x2y'' + xy' + y = sec(ln(x))
y1 = cos(ln(x)), y2 = sin(ln(x))

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 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.

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