Answer:
Step-by-step explanation:
The general solution will be the sum of the complementary solution and the particular solution:
In order to find the complementary solution you need to solve:
Using the characteristic equation, we may have three cases:
Real roots:
Repeated roots:
Complex roots:
Hence:
Solving for 
:
Since we got complex roots, the complementary solution will be given by:
Now using undetermined coefficients, the particular solution is of the form:
Note: 
was multiplied by x to account for 
and 
in the complementary solution.
Find the second derivative of in order to find the constants 
and 
:
Substitute the particular solution into the differential equation:
Simplifying:
Equate the coefficients of and on both sides of the equation:
So:
Substitute the value of the constants into the particular equation:
Therefore, the general solution is:
Answer:
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Step-by-step explanation:
One inch of board is left
if you subtract the two 3 inches pieces from the board
the further subtract the 24 inches from the three 8 inches pieces you get 31-30
We know that 16 cups are in 1 gallon
We also know that 10 servings = 2 cups
Now that means 80 servings = 1 gallon
That means we need 320 / 80=4
It is A 4 gallons
Hope this helps
