Find the first four terms in the Taylor series expansion of the
solution to
a. y′(x)=y(x)−x,y(0)=2.
b. y′(x)=2xy(x)−x3,y(0)=1.
c. (1+x)y′(x)=py(x),y(0)=1.
d. y′(x) = ?x2 + y2(x), y(0) = 1.
e. y′′(x)−2xy′(x)+2y(x)=0,y(0)=1,y′(0)=0.
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’ +
x2y = 0; y(0) = 1,
y’(0) = 1.
What do you expect the radius of convergence to be? Why?
please show all steps
Use the definition of Taylor series to find the first three
nonzero terms of the Taylor series (centered at c) for the
function f.
f(x) = 7 tan x, c = 9π
use the definition of the Taylor series to find the first four
nonzero terms of the series for f(x) centered at x = a
a) f(x) = xe^x, a = 0
b) f(x) = sin (x), a = π/6
Find the first four nonzero terms in a power series expansion
about x = 0 for a general solution to the given differential
equation
(x2 + 7)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
w'' - 6x2 w' + w = 0
Find the first four nonzero terms in a power series expansion
about x 0 for a general solution to the given differential equation
with the given value for x0=2.
(4x^2)y''-3y'+5y=0