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Unformatted text preview: t=10? 4 Problem 3. a) Let dx dt =5 x + 2 x 3 . Find the equilibrium solutions. Which ones are stable? b) Suppose that a motor boat is moving at 100 m/s when the motor quits. After 20 seconds, the boat has slowed to 10 m/s. Assume the resistance is proportional to its speed. Hence we have the diﬀerential equation for the speed v : dv dt =kv. How far will the boat coast? c) Use Euler with stepsize . 5 to estimate y (2) for dy dx = x 2 + y 3 , y (1) = 0 . 5 Problem 4. a) Solve the equation y 003 y10 = 0 with initial conditions y (0) = 3 , y (0) =1 . b) Solve the equation 5 z 22 z + 10 = 0 . c) Solve 9 y 00 + 6 y + 25 y = 0 , y (0) = 2 , y (0) = 1 6...
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This note was uploaded on 01/18/2009 for the course MATH 216 taught by Professor Stenstones? during the Spring '07 term at University of Michigan.
 Spring '07
 Stenstones?
 Math

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