Question

Use the power series method to find the solution of the initial value problem. Write the first eight nonzero terms of the power series centered at x = 0.

y′′= e^y, y(0) = 0, y′(0) = −1

Answer #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.

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

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 at least four non-zero terms in a power series expansion of
the solution to the initial value problem:
y'' + xy' + e^x y = 1-x^3
y(0) = 1, y'(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

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

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

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

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'' − xy' − 3y = 0
y1 = 1 + 3/2x^2+...
y2= x +....

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