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Initial Condition

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AP Calculus AB/BC

Definition

The starting value or values of a function or system at the beginning of a given scenario.

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Subjects (11)

Practice Questions (14)

Find the particular solution to the differential equation y' = 2cos(x) with the initial condition y(0) = 3.
Given the differential equation y' = 4x - 6, find the solution that satisfies the initial condition y(2) = 5.
Given the differential equation y' = -2/x, find the particular solution that satisfies the initial condition y(1) = 2.
Find the solution to the differential equation y' = 1/(x^2) with the initial condition y(1) = 1.
Given the differential equation y' = 2e^(2x), find the solution that satisfies the initial condition y(0) = 2.
Given the differential equation y' = 2x - y, find the particular solution that satisfies the initial condition y(0) = 1.
Given the differential equation dy/dx = x^2 + y and the initial condition y(1) = 3, identify the initial x, initial y, and slope values for the first step of Euler's method.
Solve the differential equation: dy/dx = 4e^x, given the initial condition y(0) = 1.
Solve the differential equation: dy/dx = 2sin(x), given the initial condition y(0) = 0.
Solve the differential equation: dy/dx = 5x^4, given the initial condition y(1) = 10.
Solve the differential equation: dy/dx = 1/x^2, given the initial condition y(1) = 2.
The solution to the differential equation dy/dx = 5y with an initial condition y(0) = 2 is given by:
The solution to the differential equation dy/dx = 0.5y with an initial condition y(0) = 10 is given by:
The solution to the differential equation dy/dx = -0.5y with an initial condition y(0) = 8 is given by:

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