Front

What is a differential equation?

Back

A differential equation is a mathematical equation that relates a function with its derivatives. It describes how a quantity changes over time or space.

Front

What does the notation dy/dx represent?

Back

The notation dy/dx represents the derivative of y with respect to x, indicating the rate of change of y as x changes.

Tags

CCSS.HSF.LE.B.5

Front

What is a slope field?

Back

A slope field is a graphical representation of the solutions to a first-order differential equation. It consists of a grid of line segments that represent the slope of the solution curve at various points.

Front

How do you find the general solution of a differential equation?

Back

To find the general solution of a differential equation, you integrate the equation with respect to the dependent variable and include a constant of integration.

Front

What is the initial condition in a differential equation?

Back

An initial condition is a value that specifies the state of the system at a particular point, allowing for the determination of a specific solution to the differential equation.

Front

Back

Front

What is the significance of the slope in a slope field?

Back

The slope in a slope field indicates the direction and steepness of the solution curve at that point. It helps visualize the behavior of solutions.

Front

What does it mean for a solution to be increasing or decreasing?

Back

A solution is increasing if its derivative (slope) is positive, and decreasing if its derivative is negative.

Front

Back

Front

What is the relationship between the slope field and the solutions of a differential equation?

Back

The slope field provides a visual representation of the solutions, showing how they behave and change over the domain.