Differential Equations Flashcard
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
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 in relation to another quantity.
2.
FLASHCARD QUESTION
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
3.
FLASHCARD QUESTION
Front
What is the general solution of a first-order linear differential equation?
Back
The general solution of a first-order linear differential equation is of the form y = Ce^{rac{1}{m}x} + f(x), where C is a constant and f(x) is a particular solution.
4.
FLASHCARD QUESTION
Front
What is the purpose of initial conditions in solving differential equations?
Back
Initial conditions are used to find the particular solution of a differential equation by providing specific values for the function and its derivatives at a given point.
5.
FLASHCARD QUESTION
Front
How do you solve a separable differential equation?
Back
To solve a separable differential equation, you separate the variables by rearranging the equation into the form g(y)dy = h(x)dx, then integrate both sides.
6.
FLASHCARD QUESTION
Front
What is the slope field of a differential equation?
Back
A slope field is a graphical representation of the solutions of a differential equation, showing the slope of the solution curves at various points in the plane.
Tags
CCSS.8.EE.C.8B
7.
FLASHCARD QUESTION
Front
What is the significance of the constant 'C' in the general solution of a differential equation?
Back
The constant 'C' represents the family of solutions to the differential equation, indicating that there are infinitely many solutions differing by a constant.
Tags
CCSS.HSA-REI.B.4B
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