Unit 7: Differential Equations

The equation $$y=e^x-2$$ is a particular solution to which of the following differential equations?

Which of the following is a solution to the differential equation y'' + y = 0?

Which of the following is the slope field for the differential equation $$\frac{\text{d}y}{\text{d}x}=xy$$ ?

The slope field shown above corresponds to which of the following differential equations?

In which quadrant(s) is the differential equation $$\frac{dy}{dx} = \frac{xy^2}{e^y}$$ always negative?

If $$\frac{dy}{dx} = 4xy$$ and if $$y = 1$$ when $$x = 2$$ then $$y =$$

Consider the general solution y = f(x) to the differential equation $$\frac{dy}{dx} = \frac{y}{x}$$ . To what function family does f(x) belongs to?

If $$\frac{dP}{dt} = P - 3$$ and P(4) = 2 then an expression for P(t) is

If $$\frac{dy}{dx} = ky$$ where k is a constant, and y(0) = 100, then y(3) is

The rate at which a chemical element decays is directly proportional to the amount of the element remaining. Suppose 20 grams of the element is present at t = 0. At t = 2, 5 grams of the element is present. Which of the following equations can be used to find the correct constant of proportionality, k?