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Differential Equation Application

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1) Find the equilibrium solution of the differential equation:

Dy/dt = 3y(1-(1/2)y)

Sketch the slope field and use it to determine whether each equilibrium is stable or unstable.

2) Consider the initial value problem
Y^1 = 4 - y^2, y(0) = 1

Use the Euler's method with 5 steps to estimate y(1). Sketch the field and use it to determine whether the estimate is an overestimate or an underestimate.

3) Find the Taylor polynomial of degree 4 as an approximation of the Solution of the initial problem.

Y^1 - 2x^2 + y^2 = 0, y (0) = 2

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This solutions includes step by step solutions to questions on equilibrium solutions, Euler's solutions and Taylor polynomial of degree 4 for a differential equation.

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