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2. (2.2, #4) (2 pts) Solve the following differential equation in implicit form: ty = (1-y2)/2 3. (3 pts) Consider the initial value problem 3t2 3y2-12 (a) Solve the initial value problem in implicit form (b) Explain why this initial value problem has a local solution (c) For which values of y does the solution have a vertical tangent? (d) Use your answer to (c) to determine the largest interval for which the solution is valid 4. (2.3, #1) (3 pts) Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L/min, the well-stirred solution flowing out at the same rate Find the time that will elapse before the concentration of the dye in the tank reaches 1% of its original value.
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