What is the solution of the associated homogeneous equation y'' + y = 0

Step-by-step explanation:

To find the solution of a given differential equation ay''+by'+cy=0, a≠0, you have to consider the quadratic polynomial ax²+bx+c=0, called the characteristic polynomial.  

Using the quadratic formula, this polynomial will always have one or two roots, for example r and s. The general solution of the differential equation is:

, if the roots r and s are real numbers and r≠s.

, if r=s is real.

, if the roots r and s are complex numbers α+βi and  α−βi

.

In this case, the characteristic polynomial is:

Since the roots are complex numbers, with α=0 and β=1, then the answer is:

answer

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step-by-step explanation:

x= cost per bracelet

number of bracelets * x + shipping charge = total cost

so

9x+9=72