ProblemSet_1 - Suppose the ambient temperature is 70...

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GE 207K PROBLEM SET 1 1) Solve b ay dt dy + - = , a & b are positive numbers 2) Equation of Motion Solve 5 8 . 9 v dt dv - = , v(0)=0 3) Consider a population p of field mice that grows at a rate proportional to the current population, so that dp/dt = rp, p(0)=p 0 a) Solve the differential equation b) Find r if the population doubles in 30 days, if t is measured in months. 4) Newton’s law of cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (ambient temperature).
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Unformatted text preview: Suppose the ambient temperature is 70 degrees Fahrenheit and that the rate constant is 0.05 (min)-1. Write a differential equation for the temperature of the object at any time. 5) Consider an electric circuit containing a capacitor, resistor, and battery. The charge Q(t) satisfies the equation V C Q dt dQ R = + , R=resistance, C=capacitance, V= voltage const. If Q(0) = 0, find Q(t) at any time t. Solve for y : 6) ty’ + 2y = sint 7) y’ – y = 2te 2t y(0)=1 8) ty’ + (t + 1)y = t y(ln2) = 1 t > 0...
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