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 January 21st, 2011, 02:00 PM #1 Senior Member   Joined: Jan 2009 Posts: 344 Thanks: 3 Help with differential equation problem A person's weight depends on both the number of Calories consumed and the energy used. Moreover the amount of energy used depends on a person's weight - the average amount of energy used by a person is 17.5 Calories per pound per day. So, the more weight a person loses, the less energy a person uses (assuming the person maintains a Constant Level of activity). An equation that can be used to model weight loss is; dw/dt = c/3500 - 17.5w/3500. Where w, is the person's weight (in pounds), t is the time in days, and c is the constant daily consumption. [a] Find the general Solution of the differential equation; dw/dt = c/3500 - 17.5w/3500. My Answer: $\text{w= (c/3500)*t-(17.5/3500)w[t] + c}$ Wolframalpha answer: $w[t]= 0.0571429ce^{(t/10)}+c*e^{(-0.005t)}$ I don't what you mean by using e^(-0.005t) as an integrating factor. [b] Consider a person who weighs 180 pounds and begins a diet of 2500 Calories per day. How long will it take the person to lose 10 pounds? How long will it take the person to lose 35 pounds?
 January 21st, 2011, 05:53 PM #2 Global Moderator   Joined: Dec 2006 Posts: 18,716 Thanks: 1532 Can you try solving the differential equation by using e^(.005t) as an integrating factor, and then post your work?

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explain the dw/dt= C/3500-17.5w /3500

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