Calc AB Unit 7 Differential Equations Flashcards

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Calculus

Differential Equations

AP Calculus AB

Unit 7: Differential Equations

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7 Terms

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Differential Equation

An equation with a derivative, usually in Leibniz notation dy/dx

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Separable Differential Equation (solving)

Separate the differential equation into dy and dx parts such as Ady = Bdx, where A and B are in terms of y and x respectively.

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v(t) = ? (formula in terms of acceleration)

v(t) = v_0 + at

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x(t) = ? (formula in terms of acceleration and velocity)

x(t) = x_0 + v_0t + at²/2

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Exponential Growth Differential Equation

dy/dt = ky, where k is a proportional constant

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Slope Field

Grid of dots with lines that represent the slope of that function if it were to pass through that point, such as this slope field of dy/dx = (y-1)/x² from the 2008 AB Exam

<p>Grid of dots with lines that represent the slope of that function if it were to pass through that point, such as this slope field of dy/dx = (y-1)/x² from the 2008 AB Exam</p>
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Exponential Growth/Decay solution?

y = Ae^(kt), where A is the initial y value