consider the differential equation x3y ''' + 8x2y '' + 9xy ' − 9y = 0; x, x−3, x−3 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−3, x−3 ln(x)) = ≠ 0 for 0 < x < [infinity].

Verifying that a given expression is a solution to the equation is just a matter of plugging in the expression and its derivatives, and making sure that the given expressions are indeed linearly independent.

For example, if y = x, then y' = 1 and the other derivatives vanish. So the DE after substitution reduces to

9x - 9x = 0

which is true for all 0 < x < ∞.

To check for linear independence, you compute the Wronskian, which, judging by what you wrote, you've already done...

a = 3.14

b = 18

c = 18/5 or 3.6 or 3 3/5

step-by-step explanation:

a thesis statement is not a fact or a question

step-by-step explanation:

a thesis statement is a topic it is not a fact or a question