Use power series to find two linearly independent solutions
centered at the point x=0
1) y'' + 2y' - 2y = 0
2) 2x2y'' + x(x-1)y' - 2y = 0
please show work, thank you!
a) Find the Taylor series for sinh(x) (centered at x=0), for e^x
(centered at x=0) and hyperbolic sine and hyperbolic cosine.
b) same as a but cosh(x) instead
Find a power series for the following function, centered at c =
0, and determine the interval of convergent
f(x)=(3x−8)/(3x^2+5x−2)
(show all the works please)
Find the power series solution for the equation y'' + (sinx)y =
x; y(0) = 0; y'(0) = 1
Provide the recurrence relation for the coefficients and derive
at least 3 non-zero terms of the solution.
Consider the equation y''− (sin x)y = 0.
Find the general solution as a power series centered at x = 0.
Write the first six nonzero terms of the solution. Write the two
linearly independent solutions that form the general solution.
Differential Equations
Find a power series for the function, centered at
c.
f(x) =
3
2x − 1
, c = 2
f(x) =
∞
n = 0
Determine the interval of convergence. (Enter your answer using
interval notation.)