Calc AB Unit 7 Differential Equations Flashcards

Differential Equation

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

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.

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

v(t) = v_0 + at

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

x(t) = x_0 + v_0t + at²/2

Exponential Growth Differential Equation

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

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

Exponential Growth/Decay solution?

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