In: Advanced Math

Find two power series solutions of the given differential equation about the point x=0

*(x^2+2) y″+3xy'-y=0*

1.(4-x^2)y''+2y=0, x0=0
(a) Seek power series solutions of the given differential
equation about the given point x0; find the recurrence
relation.
(b) Find the first four terms in each of two solutions y1 and y2
(unless the series terminates sooner)
. (c) By evaluating the Wronskian W(y1, y2)(x0), show that y1
and y2 form a fundamental set of solutions.
(d) If possible, find the general term in each solution.

a. Seek power series solutions of the given differential
equation about the given point x0; find the recurrence relation
that the coefficients must satisfy.
b. Find the first four nonzero terms in each of two solutions y1
and y2 (unless the series terminates sooner).
y''-xy'-y=0 ; x0=0

(a) Seek power series solutions of the given differential
equation about the given point x0;
find the recurrence relation.
(b) Find the first four terms in each of two solutions y1 and y2
(unless the series terminates
sooner).
(c) By evaluating the Wronskian W(y1, y2)(x0), show that y1 and y2
form a fundamental set
of solutions.
(d) If possible, find the general term in each solution.
1. y''-y=0, x0=0
2. y''-xy'-y=0, x0=0
3. (4-x^2)y''+2y=0, x0=0
4. 2y''+(x+1)y'+3y=0, x0=2

Find two linearly independent power series solutions of the
given differential equation about the ordinary point x=0.
y''-2xy=0

find two power series solutions of 2x^2 y''-xy'+(x+1)y=0 about
the center at the point x=0

Find two solutions in Power Series for the differential equation (x
- 1) and "+ 3y = 0 around the ordinary point x = 0.

Find the general power series solution for the differential
equation
2x^2y''-xy'+(x^2 +1) y =0 about x=0
(Answer should be given to the x^4+r term)

Find two power series solutions of the following differential
equations.
y'' - xy' = 0

Find a recurrence relation fot the power series solutions of
differential equation y''-2xy'+8y=0 about the ordinary point
x=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.

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