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.
Find the first four nonzero terms in a power series expansion of
the solution to the given initial value problem.
3y"-2e6xy'+4(cosx)y=0; y(0)=1, y'(0)=1
Type an expression that includes all terms up to order 3.
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 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
Find at least the first four nonzero terms of the power series
expansion around x = 0 for the general solution of the differential
equation y"+ x²y'- xy = 0.