Differential Equations
(dP/dt) = 1.4P(1 - (P/4100))
For what values of P is the population increasing?
What is (0, 4100)?
The solutions of a first derivative function represented on a graph
What is slope field?
(dy/dx) = 3x2y2
Solve the differential equation
What is y = -1/(x3 + C)?
(dP/dt) = 0.4P - .001P2, P(0) = 80
What is the carrying capacity?
What is 400?
y' - y = 8ex
Solve the differential equation
What is y = 8xex + Cex?
y = (-5/2)xcosx
y = (5/2)xsinx
y = 5sinx
Which one of these is a solution of the differential equation y'' + y = 5sin(x)?
What is y = (-5/2)xcosx?
Use this link and look at example 1
https://www.shmoop.com/differential-equations/equilibrium-solutions-examples.html
Where are the equilibrium solutions? If there are none simply guess none.
What is y=10 and y=20?
(dy/dx) = (x/y), y(0) = -3
Solve the differential equation using the initial condition
What is y = -√(x2 + 9)?
(dP/dt) = 0.2P - .001P2
What is P'(0)?
What is P'(0) = 6.4?
x2y' +2xy = ln(x), y(1) = 2
Solve the initial-value problem
What is y = (ln(x)/x) - (1/x) + (3/x2)?
A fresh cup of coffee is 91 degrees C sitting in a room that is 20 degrees C. Newton's Law of Cooling states that an object's rate of cooling is proportional to the temperature difference between the object and its surrounding environment. Write a differential equation for Newton's Law of Cooling for this situation using t as the independent variable, y as the dependent variable, R as the room temperature, and k as a proportionality constant). Also state the initial condition.
What is (dy/dt) = k(y-R)?
What is y(0) = 91?
Use Euler's method with step size 0.5 to approximate y(6) given the initial-value problem
y' = y - 4x, y(4) = 1
(Round answer to 4 decimal places)
What is y(6) = -68.1875?
A tank contains 6000 L of brine with 17 kg of dissolved salt. Pure water enters the tank at a rate of 60L/min. The solution is mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes?
What is y = 17/(e.01t)?
A population grows according to a logistic model with an initial population of 500 and a carrying capacity of 5,000. If the population increases to 1,250 after 1 year, what will the population be after an additional 3 years?
What is 4500?
A tank with a capacity of 4000 L is full of a mixture of water and chlorine with a concentration of 0.005 g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 40 L/s. The mixture is kept stirred and is pumped out at a rate of 100 L/s. Find the amount of chlorine in the tank as a function of time.
What is y = 20(1-(3t/200))(5/3)?