Slope Fields and Verify Differential Solutions
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a slope field?
Back
A slope field is a graphical representation of the solutions to a first-order differential equation, showing the slopes of the solution curves at various points in the plane.
2.
FLASHCARD QUESTION
Front
What does the derivative dy/dx = -x represent in a slope field?
Back
It represents a slope field where the slope of the tangent line at any point (x, y) is equal to the negative of the x-coordinate.
3.
FLASHCARD QUESTION
Front
How do you verify if a function is a solution to a differential equation?
Back
To verify, substitute the function into the differential equation and check if both sides are equal.
4.
FLASHCARD QUESTION
Front
What is the general form of a first-order differential equation?
Back
The general form is dy/dx = f(x, y), where f is a function of x and y.
5.
FLASHCARD QUESTION
Front
What does dy/dx = 2x indicate about the slope at any point?
Back
It indicates that the slope of the solution curve at any point (x, y) is equal to twice the x-coordinate.
6.
FLASHCARD QUESTION
Front
What is the significance of the solution y = e^{3x} in the context of differential equations?
Back
It is an exponential solution that can be used to verify if it satisfies a given differential equation.
7.
FLASHCARD QUESTION
Front
What does the notation y'' - 2y' = 3y represent?
Back
It represents a second-order linear differential equation involving the function y and its first and second derivatives.
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