X^3y ''' + 10x^2y '' + 16xy ' − 16y = 0; x, x^−4, x^−4 ln x, (0, [infinity])

Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.

The functions satisfy the differential equation and are linearly independent since

W(x, x−4, x−4 ln x) = ≠ 0 for 0 < x < [infinity].

Form the general solution.

y=

Verifying that a solution satisifes the ODE is a matter of substituting the solution into the ODE. For example,

The Wronskian for these solutions is

which is non-zero for all , so the solutions are indeed linearly independent.

The general solution is then

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720

22, 28, 34, 40, 46

b)   f(n) = 6n + 16

n = what is the number of the row ( 22 would be row 1) so if we replaced n with 1, we would get 22

c)   the 14th row will have 100 seats

(1)   (2)   (3)   (4)   (5)   (6)   (7)   (8)   (9)   (10) (11) (12) (13) (14)

22 | 28 | 34 | 40 | 46 | 52 | 58 | 64 | 70 | 76 | 82 | 88 | 94 | 100