2) The roots of the auxiliary equation are (enter answers as a comma separated l

Question

2) The roots of the auxiliary equation are  (enter answers as a comma separated list). _________________

3) A fundamental set of solutions is ________________

Given the third order homogeneous constant coefficient equation y1,y2,y3) = 0 2) The roots of the auxiliary equation are (enter answers as a comma separated list). _________________ 3) A fundamental set of solutions is ________________ (Enter the fundamental set as a commas separated list ar^3 +br^2 +cr + d = {y +3y -5y -39y} = 0 1) the auxiliary equation is

Explanation / Answer

We make the assumption that the solution has the form

       y = ert

Then

        y' = rert         y'' = r2ert         y''' = r3ert

Substituting back into the differential equation, we get

        r3ert + 3(r2ert) - 5rert - 39ert   = 0

Dividing by ert, we get the auxilliary equation

        r3+ 3r2 - 5r - 39 = 0

We can factor to find the roots of the equation. A calculator can efficiently do this, or you can use the rational root theorem to get

       (r2 + 6r + 13)

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