**Unformatted text preview: **. 10. Find a non-constant solution of the initial value problem ˙ y = y 1 / 3 , y (0) = 0, using separation of variables. Note that the constant function y ( t ) = 0 also solves the initial value problem. Hence, an initial value problem need not have a unique solution. 11. Solve the equation for Newton’s law of cooling leaving M and k unknown. 12. After 10 minutes in Jean-Luc’s ready room, his tea has cooled to 40 ◦ Celsius. The room temperature is 25 ◦ Celsius. If k = 1, what was the initial temperature of the tea? 13. Solve the logistic equation ˙ y = ky ( M-y ). (This is a somewhat more reasonable population model in most cases than the simpler ˙ y = ky .) Sketch the graph of the solution to this equation when y (0) = 1 / 2....

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- Fall '07
- JonathanRogawski
- Math, Differential Equations, Calculus, Equations, Derivative