Question

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

Answer #1

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 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 at least the first six non-zero terms of the general power
series solution, centered at the ordinary point ?=0, of the given
differential equation. Write your answer in standard form.
?''−?^2 ?'+?=0

Find at least the first 3 non-zero terms of each series solution
for the particular solution and the two homogeneous solutions of
the differential equation:
y'' - sin(x)y = cos(x)

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+6)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.
(x^2+19)y``+y=0

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

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