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19 Cards in this Set
- Front
- Back
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Order:
1. y^I=y^2-3t 2. y^I+y^II=4y-t^2 3. y*y^III=5 |
1. First order (y^I) y^I=y^2-3t
2. Second order (y^II) y^I+y^II=4y-t^2 3. Third order (y^III) y*y^III=5 |
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Linear or Nonlinear:
1. y^II+2y^I+y=t^2 2. ty^III+sin(t)y^I=y/(t+1) 3. y*y^II+y^III=t 4. y^4+sin(y^I)+3ty=0 |
1. linear y^II+2y^I+y=t^2
2. linear ty^III+sin(t)y^I=y/(t+1) 3. nonlinear y*y^II+y^III=t 4. nonlinear y^4+sin(y^I)+3ty=0 Linear is of the form Ay^n+By^(n-1)+...+Cy=D Where A,B,C,D are each something with only t variables) |
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Using maple/matlab what commands would you give to create a graph plotting the "slope field" (AKA Directional Field) of the equation
y^I=3sin(t)+1+y |
with(plots);
fieldplot([1,3*sin(t)+1+y],t=-4..4,y=-4..4,arrows=line,fieldstrength=fixed(0.5)); |
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What is a Slope Field?
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A Directional Field
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What is a Differential Equation?
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What is the Order of a Differential Equation?
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What is a Initial Value?
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What is a Directional Field (AKA Slope Field)?
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What is the difference between Linear and Nonlinear?
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What is an Exact Equation?
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What is an Integrating Factor?
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What is an Integral Curve?
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What does it mean to be Separable?
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What does it mean to be Autonomous?
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What is Exponential Growth?
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What does it mean to be Asymptotically Stable?
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What is Logistic Growth?
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What is an Unstable Equilibrium?
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What does it mean to be homogeneous?
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