Substituting this into the other ODE gives
Since , it follows that
. The ODE in
has characteristic equation
with roots , admitting the characteristic solution
From the initial conditions we get
So we have
Take the derivative and multiply it by -1/4 to get the solution for :
Answer:
The length of the border is approximately 4 feet.
Step-by-step explanation:
Since the garden has a circular border we can apply the formula for the circle's length, which is shown below:
Where the radius is half the diameter. The diameter is the distance between two points in the circle going through the center, therefore for this garden the diameter is 1.2 feet and the radius is 0.6 feet. Applying this to the formula gives us:
The length of the border is approximately 4 feet.