Differential Equations Problems
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Questions and Answers

What is the general form of a differential equation that models the growth of a population that doubles every hour?

dy/dt = ky, where k is a constant

What is the particular solution to the differential equation dy/dt = 2y with the initial condition y(0) = 5?

y = 5e^(2t)

What is the general form of a separable differential equation?

dy/dt = f(y)g(t)

What is the half-life of a radioactive substance that decays at a rate proportional to its mass?

<p>The half-life is the time it takes for the mass to decrease by half, given by the formula t_half = ln(2) / k, where k is the decay rate.</p> Signup and view all the answers

What is the formula for the volume of a solid generated by revolving a region around the x-axis?

<p>V = π ∫[a, b] (f(x))^2 dx</p> Signup and view all the answers

What is the shape of the cross section of a solid formed by revolving the region between y = √x and y = x about the y-axis?

<p>A washer</p> Signup and view all the answers

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