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Slope fields
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Slope fields
Basic Concepts: Order and solutions to differential equations
Related Concepts: Separable equations
Lessons
Slope fields, also called directional fields or vector fields, are graphical representations of first-order differential equations.
Slope Fields consist of a bunch of lines indicating the slope of y with respect to x, or dxdy
Slope Fields consist of a bunch of lines indicating the slope of y with respect to x, or dxdy
- IntroductionWhat are Slope Fields?
- 1.Understanding Slope Fields
Find the directional field for the following equations:a)dxdy=xy−xb)dxdy=(y+1)x2 - 2.Determining the Equation from a Slope Field
Which equation best corresponds to the following slope field?
i. dxdy=y−2
ii. dxdy=xy−2
iii. dxdy=x+1
iv. dxdy=−x+1
- 3.Which equation best corresponds to the following slope field?
i. dxdy=xy−2
ii. dxdy=−xy
iii. dxdy=2x+y
iv. dxdy=xy−3
- 4.Given the differential equation and its resulting slope field:
dxdy=2y(y−3)
Draw a solution to the following differential equation using the following initial value conditions:a)y(−2)=1b)y(0)=4c)y(1)=3