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Function Notation

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Verified questions

DIFFERENTIAL EQUATIONS

determine the general solution of the given differential equation.y(4)−y=3t+cost

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DIFFERENTIAL EQUATIONS

determine the values ofα, if any, for which all solutions tend to zero as t→∞; also determine the values ofα, if any, for which all (nonzero) solutions become unbounded as t→∞.y"−(2α−1)y'+α(α−1)y=0

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DIFFERENTIAL EQUATIONS

Suppose that a motorboat is moving at $40$ ft/s when its motor suddenly quits, and that $10$ s later the boat has slowed to $20$ ft/s. Assume that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?

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DIFFERENTIAL EQUATIONS

A spring is stretched 10 cm by a force of 3 N. A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 N when the velocity of the mass is 5 m/s. If the mass is pulled down 5 cm below its equilibrium position and given an initial downward velocity of 10 cm/s, determine its position u at any time t. Find the quasi frequency μ and the ratio of μ to the natural frequency of the corresponding undamped motion.

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