Section 5.2 Problem 13: Solve the initial value problem.

The characteristic equation is

with complex roots r = -7 ± i, so the characteristic solution is

whose derivative is

Use the initial conditions to solve for the constants:

Then the particular solution is

2? if not the correct answer you might need to provide more information

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.