Podcast
Questions and Answers
Which of the following best describes an ordinary differential equation?
Which of the following best describes an ordinary differential equation?
- An equation involving known constants and their derivatives
- An equation involving known functions and their derivatives
- An equation involving an unknown constant and its derivatives
- An equation involving an unknown function and its derivatives (correct)
What is the order of the differential equation dy/dt = y - t?
What is the order of the differential equation dy/dt = y - t?
- Fourth order
- Second order
- Third order
- First order (correct)
Which of the following equations is a second-order differential equation?
Which of the following equations is a second-order differential equation?
- $y' = y^2 - ty$
- $yy'' + t^2y = \cos(t)$ (correct)
- $y = y^2 - t$
- $yy' + 4y = e^{-3t}$
What will be covered in this chapter according to Section 2.1?
What will be covered in this chapter according to Section 2.1?
What is the unknown function in the equation dy/dt = y - t?
What is the unknown function in the equation dy/dt = y - t?
Which of the following equations is a first-order differential equation?
Which of the following equations is a first-order differential equation?
What is the order of the differential equation $\frac{{\partial^2w}},{{\partial t^2}} = c^2\frac{{\partial^2w}},{{\partial x^2}}$?
What is the order of the differential equation $\frac{{\partial^2w}},{{\partial t^2}} = c^2\frac{{\partial^2w}},{{\partial x^2}}$?
Which of the following is the definition of an initial value problem?
Which of the following is the definition of an initial value problem?
What is the interval of existence of the solution to the initial value problem $y' = y^2$, $y(0) = 1$?
What is the interval of existence of the solution to the initial value problem $y' = y^2$, $y(0) = 1$?
What is the general solution of the differential equation $y' = x + y$?
What is the general solution of the differential equation $y' = x + y$?
What is the interval of existence of the solution to the differential equation $s' = \sqrt{r}$?
What is the interval of existence of the solution to the differential equation $s' = \sqrt{r}$?
Verify that $x(s) = 2 - Ce^{-s}$ is a solution of the differential equation $x' = 2 - x$. What is the solution that satisfies the initial condition $x(0) = 1$?
Verify that $x(s) = 2 - Ce^{-s}$ is a solution of the differential equation $x' = 2 - x$. What is the solution that satisfies the initial condition $x(0) = 1$?
What is the geometric interpretation of a differential equation?
What is the geometric interpretation of a differential equation?
What is a direction field in the context of a differential equation?
What is a direction field in the context of a differential equation?
Which type of differential equation involves partial derivatives of an unknown function of more than one independent variable?
Which type of differential equation involves partial derivatives of an unknown function of more than one independent variable?
What is the normal form for a first-order differential equation?
What is the normal form for a first-order differential equation?
How can we determine if a given function is a solution to a differential equation?
How can we determine if a given function is a solution to a differential equation?
What is the general solution to the first-order equation $y'(t) = -2ty$?
What is the general solution to the first-order equation $y'(t) = -2ty$?
What is the general solution to the equation $y^{(n)} = f(t, y, y', ..., y^{(n-1)})$?
What is the general solution to the equation $y^{(n)} = f(t, y, y', ..., y^{(n-1)})$?
Is the function $y(t) = \cos(t)$ a solution to the differential equation $y' = 1 + y^2$?
Is the function $y(t) = \cos(t)$ a solution to the differential equation $y' = 1 + y^2$?
If $y(t) = -\frac{1},{t - C}$ is a general solution of $y' = y^2$, what is the particular solution satisfying $y(0) = 1$?
If $y(t) = -\frac{1},{t - C}$ is a general solution of $y' = y^2$, what is the particular solution satisfying $y(0) = 1$?
Which of the following best describes the use of computer-generated direction fields in understanding differential equations?
Which of the following best describes the use of computer-generated direction fields in understanding differential equations?
In the context of differential equations, what does the slope of the solution curve represent?
In the context of differential equations, what does the slope of the solution curve represent?
What does finding a solution to a differential equation represent geometrically?
What does finding a solution to a differential equation represent geometrically?
Which equation represents the direction field shown in Figure 4?
Which equation represents the direction field shown in Figure 4?
What does the solution curve of $y' = y, y(0) = 1$ look like in relation to the direction field?
What does the solution curve of $y' = y, y(0) = 1$ look like in relation to the direction field?
What is the slope of the solution curve of $y' = y, y(0) = 1$ at the point (0, 1)?
What is the slope of the solution curve of $y' = y, y(0) = 1$ at the point (0, 1)?
What is the value of y(1) for the solution curve of $y' = y, y(0) = 1$?
What is the value of y(1) for the solution curve of $y' = y, y(0) = 1$?
What is the value of y(2) for the solution curve of $y' = y, y(0) = 1$?
What is the value of y(2) for the solution curve of $y' = y, y(0) = 1$?
What is the general solution to the differential equation $y' = y$?
What is the general solution to the differential equation $y' = y$?
