Question

Find the power series solution around x=0. Find the first few
nonzero terms of each solution. Power series are not necessary to
solve try older methods in addition to power series.

1) y”+x^2y=0

Answer #1

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

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.
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.
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 the Taylor series expansion
of the solution of (x 2−2x)y 00+2y = 0, y(1) = −1, y 0 (1) = 3
about x0 = 1.

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 the solution to the given initial value problem.
w''+3xw'-w=0; w(0)=8, w'(0)=0

Find first three nonzero terms, or as many as exist, in the
series expansion about x=0 for general solution to the given
equation for x>0. 5x(x-1)y''+9(x-1)y'-y=0.

Find the first four nonzero terms in a power series expansion
about x0 for a general solution to the given
differential equation with the given value for x0.
x2y''-y'+y = 0; x0 = 2

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