Question

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.

Answer #1

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

Find the first four terms in the Taylor series expansion of the
solution to
y′(x) = 2xy(x)−x3, y(0) = 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+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-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-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.
(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
(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+6)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

Use the definition of a Taylor series to find the first four
nonzero terms of the series for f(x) centered at
the given value of a. (Enter your answers as a
comma-separated list.)
f(x) = 4/(1+x), a = 2
Use the definition of a Taylor series to find the first four
nonzero terms of the series for f(x) centered at
the given value of a. (Enter your answers as a
comma-separated list.)
f(x) = 3xe^x, a = 0

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