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How do you solve the homogeneous equation (dx/dt)+(2x/(100-t))=0?
Please include constant c into the answer.
When I do this problem, the answer turns up to be x=(((t-100)e^c)^2)/2. It's showing up as incorrect for me though.
2 AnswersMathematics1 decade agoTime Constant in Newton's Law of Cooling?
In engineering, engineers often state heating/cooling problems in terms of the time constant 1/k, the reciprocal of the constant of proportionality in Newton's Law of Cooling.
Suppose that at noon, with the temperature in your house at 75 F and the outside temperature at 95 F, your air conditioner breaks down. The time constant 1/k for your house is 4 hours.
(a) What will the temperature (in degrees Fahrenheit) in your house be at 2 p.m.?
(b) How many hours after noon must pass before the temperature (in degrees Fahrenheit) in your house reaches 80 F?
My problem is that I'm not sure how the time constant is applied into the differential equation.
2 AnswersMathematics1 decade agoHow do you solve the homogeneous equation (dx/dt)+(2x/(100-t))=0?
And does this equation type have a certain name to it?
1 AnswerMathematics1 decade ago