Ordinary Diff Eq Exam Review Solutions 13

Ordinary Diff Eq Exam Review Solutions 13 - 1 Solutions and...

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Unformatted text preview: 1 Solutions and allowing implies 15 gives the equilibrium solution. The initial condition . Thus . 28. Since at for all integers we have equilibrium , none of which satisfy the initial condition . lines at Separating variables gives and integrating gives . We can solve for here using the initial condition: we get Solving for gives 29. Separating variables gives . Solving for gives condition gives . So 30. In standard form we get and integrating gives , for . The initial . so is an equilibrium solution. . Integrating we get Separating variables gives allowing . Solving for we get gives the equilibrium solution. 31. We assume the decay model bone then . Thus years , for . However, If is the age of the . Solving for gives 32. Let denote the number of Argon- atoms in the sample. Then is the number of Potassium- atoms. Let be the age of the rock. Then years ago there were atoms of Potassium- . Hence . On the other hand, . This and hence million years implies that old. 33. We need only solve years. for . We get 34. The ambient temperature is F, the temperature of the ice water. From Equation (12) we get . At we get , so and . After minutes we have and solving for gives . To find the time when we solve , with as above. We get minutes. 35. The ambient temperature is . Equation (12) gives for the temperature of the coffee at time . Since the initial temperature of the coffee is we get . Thus . The constant is determined from the temperature at a second time: so . Thus ...
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