07.08 Differential Equations Exam Part One

The rate at which a particular medication leaves an individual's bloodstream is proportional to the amount of this medication that is in the bloodstream. An individual takes 250 mg of the drug initially. The amount of medication is halved every 13 hours. Approximately how many mg of the medication remain in the individual's bloodstream after 6 hours?

182 mg

The general solution of the differential equation d y over d x equals x over y where y ≠ 0, is a family of which of the following?

Hyperbolas

Select the general solution to x dy over dx equals y over quantity 2 plus 3y period (10 points) I: 2ln|y| + 3y = ln|x| + C II: one third ln absolute value of quantity 2 plus 3y all over y close absolute value equals ln x plus C

I

Determine the value of k that will make y = 2cos(2x) a solution to ky − y ″ = y.

NOT: k = 5 MOST LIKELY: k = −3

Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true?

The slopes are all positive in Quadrant 1.

The pressure valve to a garden hose is opened, causing the hose to experience an increase in pressure. The rate of increase in pressure with respect to time, t, is proportional to the sum of the initial pressure, po, and the instantaneous pressure, p. (

dp over dt equals c times quantity p plus p sub o

A slope field is shown for which of the following differential equations?

dy over dx is equal to negative e to the power of x

Let y = f(x) be the particular solution to the differential equation dy over dx equals negative 3 times x times y cubed comma with the initial condition f(1) = 1. Which of the following gives an expression for f(x) and the domain for which the solution is valid?

f of x equals square root of quantity 1 over 3 times x squared minus 2 end quantity for open parenthesis negative infinity comma negative square root of two thirds close parenthesis and open parenthesis square root of two thirds comma infinity close parenthesis

What is the general solution to the differential equation dy over dx equals x times y plus 3 times x?

y equals e to the x squared over 2 plus C power minus 3

Which of the following is the solution to the differential equation dy over dx equals 2 times x times y all over quantity x squared plus 1 end quantity comma with the initial condition y(3) = 6?

y equals one half times x squared plus three over two