Question

7. Determine
the first 4 nonzero terms of the Taylor series for the solution
*y* = *φ*(*x*) of the given initial value
problem, *y*^{’’} +
cos(*x*)*y*^{’} +
*x*^{2}*y* = 0; *y*(0) = 1,
*y*^{’}(0) = 1.

What do you expect the radius of convergence to be? Why?

please show all steps

Answer #1

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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.

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

1- 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) = 5 cos2(x), a = 0
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) = 9xex, ...

definition of a Taylor series to find the first 4 nonzero terms
of the power series for f(x) centered at the given value of a.
f(x)=3cuberoot(x^4) , a = 8

The function f(x)=lnx has a Taylor series at a=4 . Find the
first 4 nonzero terms in the series, that is write down the Taylor
polynomial with 4 nonzero terms.

Find the first four terms in the Taylor series expansion of the
solution to
y′(x) = 2xy(x)−x3, y(0) = 1.

Question #11
Find:
The first 3 nonzero terms a Taylor series (at a = 0) of f1(x) =
sin x, f2(x) = x cos x, f3(x) = x/(2 + 2x^2 ), and f4(x) = x −
(x^3/2) − x^5
No explanation is necessary for finding: sin x, cos x, and 1/(1
− x).)

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

A) Find the first 4 nonzero terms of the Taylor series for the
given function centered at a = pi/2
B) Write the power series using summation notation
f(x) = sinx

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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